Bisection (software engineering)

Over 25,000 Expat pleasant property listings provided by licensed Singapore property brokers Welcome to Singapore Property For Sale! That includes Singapore, JB Iskandar, London, Australia, Philipiines, Cambodia Property! Cellular Apps FREE Sign Up Log in Property Agents Suggestions Welcome to OrangeTee! Singapore's Largest Property & Real Property Firm. Have the recent cooling measures been restricting you ininvesting property in Singapore? Take into account London property as anoption.

Investors will likely want to get a breakdown of the industrial properties that individuals can discover after they view the Hexacube There are actually 5 distinct levels of the complicated, plus an extra basement level. All of those ranges will provide their very own unique design, which can undoubtedly appeal to many individuals on the market. Some guests will want to try how they can take a tour of the complex. This can assist them visualize how they will arrange buildings all through these locations in only a short amount of time. This could possibly be a useful asset to house owners who must study more about how they will improve the workplace areas that they can use right here.

My point? Based on my expertise and what I have noticed, investing in property is the commonest manner for the common person to build up a big amount of wealth However is not it risky to put money into property now? Are banks nonetheless keen to do property lending? What an investor should test before committing to a property purchase How changes in laws will affect the prospects for an en bloc sale GETTING YOUR PROPERTY SOLD / LEASED? Your Property Might Be Featured Right here! Condominium For Rent – Tribeca by the Waterfront (D09) Yong An Park (D09) – Condominium For Hire The Glyndebourne (D11) – Condominium For Lease Scotts 28 (D09) – Condominium For Hire Condominium For Hire – The Balmoral (D10) Learn on for a few of the hot property within the Featured Listings under.

Solely Singapore citizens and accredited persons should buy Landed 'residential property'as outlined within the Residential Properties Act. Foreigners are eligible to purchaseunits in condominiums or flats which aren't landed dwelling homes. Foreignerswho want to purchase landed property in Singapore should first seek the approval ofthe Controller of Residential Property. Your Lawyer's Position in a Property Buy The most important mistakes Singapore property buyers and novices make Secrets of Singapore Property Gurus assessment by Way of life magazine The Laurels is a freehold apartment growth at Cairnhill Highway, Singapore (District 9). Property developer of recent apatments. 107 Tampines Highway, Singapore 535129. Search HDB Flats For Sale by Estate Industrial Properties

Should you're an expert investor, consider the "on the market by proprietor" properties. For sale by proprietor properties often current a unbelievable investment opportunity for buyers that are acquainted with this method. If you do not need to regret your New Ec launch singapore house buy, it is best to pay careful attention to the neighborhood where the house is located. Test the speedy space and see if there are a lot of properties on the market. Test for closed companies, closed faculties or numerous accessible rentals. Any of these items could level to a decline within the neighborhood. Houses for Sale Singapore Tip

In Yr 2013, c ommercial retails, shoebox residences and mass market properties continued to be the celebs of the property market. Units are snapped up in document time and at document breaking prices. Developers are having fun with overwhelming demand and consumers want more. We feel that these segments of the property market are booming is a repercussion of the property cooling measures no.6 and no. 7. With additional buyer's stamp duty imposed on residential properties, traders switch their focus to business and industrial properties. I consider every property purchasers need their property investment to appreciate in worth. In quantum field theory, and in the significant subfields of quantum electrodynamics and quantum chromodynamics, the two-body Dirac equations (TBDE) of constraint dynamics provide a three dimensional yet manifestly covariant reformulation of the Bethe–Salpeter equation for two spin-1/2 particles. Such a reformulation is necessary since without it, as shown by Nakanishi, the Bethe–Salpeter equation possesses negative-norm solutions arising from the presence of an essentially relativistic degree of freedom, the relative time. These "ghost" states have spoiled the naive interpretation of the Bethe–Salpeter equation as a quantum mechanical wave equation. The two-body Dirac equations of constraint dynamics rectify this flaw. The forms of these equations can not only be derived from quantum field theory they can also be derived purely in the context of Dirac's constraint dynamics and relativistic mechanics and quantum mechanics. Their structures, unlike the more familiar two-body Dirac equation of Breit, which is a single equation, are that of two simultaneous quantum relativistic wave equations. A single two-body Dirac equation similar to the Breit equation can be derived from the TBDE. Unlike the Breit equation, it is manifestly covariant and free from the types of singularities that prevent a strictly nonperturbative treatment of the Breit equation. In applications of the TBDE to QED, the two particles interact by way of four-vector potentials derived from the field theoretic electromagnetic interactions between the two particles. In applications to QCD, the two particles interact by way of four-vector potentials and Lorentz invariant scalar interactions, derived in part from the field theoretic chromomagnetic interactions between the quarks and in part by phenomenological considerations. As with the Breit equation a sixteen-component spinor Ψ is used.

Equations

For QED, each equation has the same structure as the ordinary one-body Dirac equation in the presence of an external electromagnetic field, given by the 4-potential $A_{\mu }$. For QCD, each equation has the same structure as the ordinary one-body Dirac equation in the presence of an external field similar to the electromagnetic field and an additional external field given by in terms of a Lorentz invariant scalar $S$. In natural units: those two-body equations have the form.

$[(\gamma _{1})_{\mu }(p_{1}-{\tilde {A}}_{1})^{\mu }+m_{1}+{\tilde {S}}_{1}]\Psi =0,$

$[(\gamma _{2})_{\mu }(p_{2}-{\tilde {A}}_{2})^{\mu }+m_{2}+{\tilde {S}}_{2}]\Psi =0.$

where, in coordinate space, p^μ is the 4-momentum, related to the 4-gradient by (the metric used here is $\eta _{\mu \nu }=(-1,1,1,1)$)

$p^{\mu }=-i{\partial \over \partial x_{\mu }}$

and γ^μ are the gamma matrices. The two-body Dirac equations (TBDE) have the property that if one of the masses becomes very large, say $m_{2}\rightarrow \infty$ then the 16-component Dirac equation reduces to the 4-component one-body Dirac equation for particle one in an external potential.

In SI units:

$[(\gamma _{1})_{\mu }(p_{1}-{\tilde {A}}_{1})^{\mu }+m_{1}c+{\tilde {S}}_{1}]\Psi =0,$

$[(\gamma _{2})_{\mu }(p_{2}-{\tilde {A}}_{2})^{\mu }+m_{2}c+{\tilde {S}}_{2}]\Psi =0.$

where c is the speed of light and

$p^{\mu }=-i\hbar {\partial \over \partial x_{\mu }}$

Natural units will be used below. A tilde symbol is used over the two sets of potentials to indicate that they may have additional gamma matrix dependencies not present in the one-body Dirac equation. Any coupling constants such as the electron charge are embodied in the vector potentials.

Constraint dynamics and the TBDE

Constraint dynamics applied to the TBDE requires a particular form of mathematical consistency: the two Dirac operators must commute with each other. This is plausible if one views the two equations as two compatible constraints on the wave function. (See the discussion below on constraint dynamics.) If the two operators did not commute, (as, e.g., with the coordinate and momentum operators $x,p$) then the constraints would not be compatible (one could not e.g., have a wave function that satisfied both $x\Psi =0$ and $p\Psi =0$). This mathematical consistency or compatibility leads to three important properties of the TBDE. The first is a condition that eliminates the dependence on the relative time in the center of momentum (c.m.) frame defined by $P=p_{1}+p_{2}=(w,{\vec {0}})$. (The variable $w$ is the total energy in the c.m. frame.) Stated another way, the relative time is eliminated in a covariant way. In particular, for the two operators to commute, the scalar and four-vector potentials can depend on the relative coordinate $x=x_{1}-x_{2}$ only through its component $x_{\perp }$ orthogonal to $P$ in which

$x_{\perp }^{\mu }=(\eta ^{\mu \nu }-P^{\mu }P^{\nu }/P^{2})x_{\nu },\,$

$P_{\mu }x_{\perp }^{\mu }=0.\,$

This implies that in the c.m. frame $x_{\perp }=(0,{\vec {x}}={\vec {x}}_{1}-{\vec {x}}_{2})$, which has zero time component.

Secondly, the mathematical consistency condition also eliminates the relative energy in the c.m. frame. It does this by imposing on each Dirac operator a structure such that in a particular combination they lead to this interaction independent form, eliminating in a covariant way the relative energy.

$P\cdot p\Psi =(-P^{0}p^{0}+{\vec {P}}\cdot p)\Psi =0.\,$

In this expression $p$ is the relative momentum having the form $(p_{1}-p_{2})/2$ for equal masses. In the c.m. frame ($P^{0}=w,{\vec {P}}={\vec {0}}$), the time component $p^{0}$ of the relative momentum, that is the relative energy, is thus eliminated. in the sense that $p^{0}\Psi =0$.

A third consequence of the mathematical consistency is that each of the world scalar ${\tilde {S}}_{i}$ and four vector ${\tilde {A}}_{i}^{\mu }$ potentials has a term with a fixed dependence on $\gamma _{1}$ and $\gamma _{2}$ in addition to the gamma matrix independent forms of $S_{i}$ and $A_{i}^{\mu }$ which appear in the ordinary one-body Dirac equation for scalar and vector potentials. These extra terms correspond to additional recoil spin-dependence not present in the one-body Dirac equation and vanish when one of the particles becomes very heavy (the so-called static limit).

More on constraint dynamics: generalized mass shell constraints

Constraint dynamics arose from the work of Dirac and Bergmann. This section shows how the elimination of relative time and energy takes place in the c.m. system for the simple system of two relativistic spinless particles. Constraint dynamics was first applied to the classical relativistic two particle system by Todorov, Kalb and Van Alstine, Komar, and Droz-Vincent. With constraint dynamics, these authors found a consistent and covariant approach to relativistic canonical Hamiltonian mechanics that also evades the Currie-Jordan-Sudarshan "No Interaction" theorem. That theorem states that without fields, one cannot have a relativistic Hamiltonian dynamics. Thus, the same covariant three-dimensional approach which allows the quantized version of constraint dynamics to remove quantum ghosts simultaneously circumvents at the classical level the C.J.S. theorem. Consider a constraint on the otherwise independent coordinate and momentum four vectors, written in the form $\phi _{i}(p,x)\approx 0$. The symbol$\approx 0$ is called a weak equality and implies that the constraint is to be imposed only after any needed Poisson brackets are performed. In the presence of such constraints, the total Hamiltonian ${\mathcal {H}}$ is obtained from the Lagrangian ${\mathcal {L}}$ by adding to the Legendre Hamiltonian $(p{\dot {x}}-{\mathcal {L}})$ the sum of the constraints times an appropriate set of Lagrange multipliers $(\lambda _{i})$.

${\mathcal {H}}=p{\dot {x}}-{\mathcal {L}}+\lambda _{i}\phi _{i}$,

This total Hamitonian is traditionally called the Dirac Hamiltonian. Constraints arise naturally from parameter invariant actions of the form

$I=\int d\tau {\mathcal {L(\tau )=}}\int d\tau ^{\prime }{\frac {d\tau }{d\tau ^{\prime }}}{\mathcal {L(\tau )=}}\int d\tau ^{\prime }{\mathcal {L(\tau }}^{\prime }{\mathcal {)}}.$

In the case of four vector and Lorentz scalar interactions for a single particle the Lagrangian is

${\mathcal {L(\tau )}}=-(m+S(x)){\sqrt {-{\dot {x}}^{2}}}+{\dot {x}}\cdot A(x)\,$

The canonical momentum is

$p={\frac {\partial {\mathcal {L}}}{\partial {\dot {x}}}}={\frac {{\mathcal {(}}m+S(x)){\dot {x}}}{\sqrt {-{\dot {x}}^{2}}}}+A(x)$

and by squaring leads to the generalized mass shell condition or generalized mass shell constraint

$(p-A)^{2}+(m+S)^{2}=0.\,$

Since, in this case, the Legendre Hamiltonian vanishes

$p\cdot {\dot {x}}-{\mathcal {L}}=0,\,$

the Dirac Hamiltonian is simply the generalized mass constraint (with no interactions it would simply be the ordinary mass shell constraint)

${\mathcal {H=\lambda }}\left[\left(p-A\right)^{2}+(m+S)^{2}\right]\equiv \lambda (p^{2}+m^{2}+\Phi (x,p)).$

One then postulates that for two bodies the Dirac Hamiltonian is the sum of two such mass shell constraints,

${\mathcal {H}}_{i}=p_{i}^{2}+m_{i}^{2}+\Phi _{i}(x_{1},x_{2},p_{1},p_{2})\approx 0,\,$

that is

${\mathcal {H}}=\lambda _{1}[p_{1}^{2}+m_{1}^{2}+\Phi _{1}(x_{1},x_{2},p_{1},p_{2})]+\lambda _{2}[p_{2}^{2}+m_{2}^{2}+\Phi _{2}(x_{1},x_{2},p_{1},p_{2})]$

$=\lambda _{1}{\mathcal {H}}_{1}+\lambda _{2}{\mathcal {H}}_{2},\,$

and that each constraint ${\mathcal {H}}_{i}$ be constant in the proper time associated with ${\mathcal {H}}$

${\mathcal {\dot {H}}}_{i}=\{{\mathcal {H}}_{i},{\mathcal {H\}\approx }}0\,$

Here the weak equality means that the Poisson bracket could result in terms proportional one of the constraints, the classical Poisson brackets for the relativistic two-body system being defined by

$\{O_{1},O_{2}\}={\frac {\partial O_{1}}{\partial x_{1}^{\mu }}}{\frac {\partial O_{2}}{\partial p_{1\mu }}}-{\frac {\partial O_{1}}{\partial p_{1}^{\mu }}}{\frac {\partial O_{2}}{\partial x_{1\mu }}}+{\frac {\partial O_{1}}{\partial x_{2}^{\mu }}}{\frac {\partial O_{2}}{\partial p_{2\mu }}}-{\frac {\partial O_{1}}{\partial p_{2}^{\mu }}}{\frac {\partial O_{2}}{\partial x_{2\mu }}}.$

To see the consequences of having each constraint be a constant of the motion, take, for example

${\mathcal {\dot {H}}}_{1}=\{{\mathcal {H}}_{1},{\mathcal {H\}=}}\lambda _{1}\{{\mathcal {H}}_{1},{\mathcal {H}}_{1}{\mathcal {\}+}}\{{\mathcal {H}}_{1},\lambda _{1}{\mathcal {\}{\mathcal {H}}}}_{2}{\mathcal {+\lambda }}_{2}\{{\mathcal {H}}_{2},{\mathcal {H}}_{1}{\mathcal {\}+}}\{{\mathcal {\lambda }}_{2},{\mathcal {H}}_{1}{\mathcal {\}H}}_{2}.$

Since $\{{\mathcal {H}}_{1},{\mathcal {H}}_{1}\}=0$ and ${\mathcal {H}}_{1}\approx 0$ and ${\mathcal {H}}_{2}\approx 0$ one has

${\mathcal {\dot {H}}}_{1}\approx {\mathcal {\lambda }}_{2}\{{\mathcal {H}}_{2},{\mathcal {H}}_{1}\}\approx 0.\,$

The simplest solution to this is

$\Phi _{1}=\Phi _{2}\equiv \Phi (x_{\perp })$

which leads to (note the equality in this case is not a weak one in that no constraint need be imposed after the Poisson bracket is worked out)

$\{{\mathcal {H}}_{2},{\mathcal {H}}_{1}\}=0\,$

(see Todorov, and Wong and Crater ) with the same $x_{\perp }$ defined above.

Quantization

In addition to replacing classical dynamical variables by their quantum counterparts, quantization of the constraint mechanics takes place by replacing the constraint on the dynamical variables with a restriction on the wave function

${\mathcal {H}}_{i}\approx 0\rightarrow {\mathcal {H}}_{i}\Psi =0$,

${\mathcal {H}}\approx 0\rightarrow {\mathcal {H}}\Psi =0$.

The first set of equations for i = 1, 2 play the role for spinless particles that the two Dirac equations play for spin-one-half particles. The classical Poisson brackets are replaced by commutators

$\{O_{1},O_{2}\}\rightarrow {\frac {1}{i}}[O_{1},O_{2}].\,$

Thus

$[{\mathcal {H}}_{2},{\mathcal {H}}_{1}]=0,\,$

and we see in this case that the constraint formalism leads to the vanishing commutator of the wave operators for the two particlein. This is the analogue of the claim stated earlier that the two Dirac operators commute with one another.

Covariant elimination of the relative energy

The vanishing of the above commutator ensures that the dynamics is independent of the relative time in the c.m. frame. In order to covariantly eliminate the relative energy, introduce the relative momentum $p$ defined by

The above definition of the relative momentum forces the orthogonality of the total momentum and the relative momentum,

$P\cdot p=0$,

which follows from taking the scalar product of either equation with $P$. From Eqs.(Template:EquationNote) and (Template:EquationNote), this relative momentum can be written in terms of $p_{1}$ and $p_{2}$ as

$p={\frac {\varepsilon _{2}}{\sqrt {-P^{2}}}}p_{1}-{\frac {\varepsilon _{1}}{\sqrt {-P^{2}}}}p_{2}$

where

$\varepsilon _{1}=-{\frac {p_{1}\cdot P}{\sqrt {-P^{2}}}}=-{\frac {P^{2}+p_{1}^{2}-p_{2}^{2}}{2{\sqrt {-P^{2}}}}}$

$\varepsilon _{2}=-{\frac {p_{2}\cdot P}{\sqrt {-P^{2}}}}=-{\frac {P^{2}+p_{2}^{2}-p_{1}^{2}}{2{\sqrt {-P^{2}}}}}$

are the projections of the momenta $p_{1}$ and $p_{2}$ along the direction of the total momentum $P$. Subtracting the two constraints ${\mathcal {H}}_{1}\Psi =0$ and ${\mathcal {H}}_{2}\Psi =0$, gives

Thus on these states $\Psi$

$\varepsilon _{1}\Psi ={\frac {-P^{2}+m_{1}^{2}-m_{2}^{2}}{2{\sqrt {-P^{2}}}}}\Psi$

$\varepsilon _{2}\Psi ={\frac {-P^{2}+m_{2}^{2}-m_{1}^{2}}{2{\sqrt {-P^{2}}}}}\Psi$ .

The equation ${\mathcal {H}}\Psi =0$ describes both the c.m. motion and the internal relative motion. To characterize the former motion, observe that since the potential $\Phi$ depends only on the difference of the two coordinates

$[P,{\mathcal {H}}]\Psi =0$.

(This does not require that $[P,\lambda _{i}]=0$ since the ${\mathcal {H}}_{i}\Psi =0$.) Thus, the total momentum $P$ is a constant of motion and $\Psi$ is an eigenstate state characterized by a total momentum $P^{\prime }$. In the c.m. system $P^{\prime }=(w,{\vec {0}}),$ with $w$ the invariant center of momentum (c.m.) energy. Thus

and so $\Psi$ is also an eigenstate of c.m. energy operators for each of the two particles,

$\varepsilon _{1}\Psi ={\frac {w^{2}+m_{1}^{2}-m_{2}^{2}}{2w}}\Psi$

$\varepsilon _{2}\Psi ={\frac {w^{2}+m_{2}^{2}-m_{1}^{2}}{2w}}\Psi$.

The relative momentum then satisfies

$p\Psi ={\frac {\varepsilon _{2}p_{1}-\varepsilon _{1}p_{2}}{w}}\Psi$,

so that

$p_{1}\Psi =\left({\frac {\varepsilon _{1}}{w}}P+p\right)\Psi$,

$p_{2}\Psi =\left({\frac {\varepsilon _{2}}{w}}P-p\right)\Psi$ ,

The above set of equations follow from the constraints ${\mathcal {H}}_{i}\Psi =0$ and the definition of the relative momenta given in Eqs.(Template:EquationNote) and (Template:EquationNote). If instead one chooses to define (for a more general choice see Horwitz),

$\varepsilon _{1}={\frac {w^{2}+m_{1}^{2}-m_{2}^{2}}{2w}},$

$\varepsilon _{2}={\frac {w^{2}+m_{2}^{2}-m_{1}^{2}}{2w}},$

$p={\frac {\varepsilon _{2}p_{1}-\varepsilon _{1}p_{2}}{w}},$

independent of the wave function, then

and it is straight forward to show that the constraint Eq.(Template:EquationNote) leads directly to

in place of $P\cdot p=0$. This conforms with the earlier claim on the vanishing of the relative energy in the c.m. frame made in conjunction with the TBDE.\ In the second choice the c.m. value of the relative energy is not defined as zero but comes from the original generalized mass shell constraints. The above equations for the relative and constituent four-momentum are the relativistic analogues of the nonrelativistic equations

${\vec {p}}={\frac {m_{2}{\vec {p}}_{1}-m_{1}{\vec {p}}_{2}}{M}}$,

${\vec {p}}_{1}={\frac {m_{1}}{M}}{\vec {P}}+{\vec {p}}$,

${\vec {p}}_{2}={\frac {m_{2}}{M}}{\vec {P}}+{\vec {p}}$.

Covariant eigenvalue equation for internal motion

Using Eqs.(Template:EquationNote),(Template:EquationNote),(Template:EquationNote), one can write ${\mathcal {H}}$ in terms of $P$ and $p$

${\mathcal {H}}\Psi =\{\lambda _{1}[-\varepsilon _{1}^{2}+m_{1}^{2}+p^{2}+\Phi (x_{\perp })]+\lambda _{2}[-\varepsilon _{2}^{2}+m_{2}^{2}+p^{2}+\Phi (x_{\perp })]\}\Psi$

where

$b^{2}(-P^{2},m_{1}^{2},m_{2}^{2})=\varepsilon _{1}^{2}-m_{1}^{2}=\varepsilon _{2}^{2}-m_{2}^{2}\ =-{\frac {1}{4P^{2}}}(P^{4}+2P^{2}(m_{1}^{2}+m_{2}^{2})+(m_{1}^{2}-m_{2}^{2})^{2})\,.$

Eq.(Template:EquationNote) contains both the total momentum $P$ [through the $b^{2}(-P^{2},m_{1}^{2},m_{2}^{2})$] and the relative momentum $p$. Using Eq. (Template:EquationNote), one obtains the eigenvalue equation

so that $b^{2}(w^{2},m_{1}^{2},m_{2}^{2})$ becomes the standard triangle function displaying exact relativistic two-body kinematics:

$b^{2}(w^{2},m_{1}^{2},m_{2}^{2})={\frac {1}{4w^{2}}}\left\{w^{4}-2w^{2}(m_{1}^{2}+m_{2}^{2})+(m_{1}^{2}-m_{2}^{2})^{2}\right\}\,.$

With the above constraint Eqs.(Template:EquationNote) on $\Psi$ then $p^{2}\Psi =p_{\perp }^{2}\Psi$ where $p_{\perp }=p-p\cdot PP/P^{2}$. This allows writing Eq. (Template:EquationNote) in the form of an eigenvalue equation

$\{p_{\perp }^{2}+\Phi (x_{\perp })\}\Psi =b^{2}(w^{2},m_{1}^{2},m_{2}^{2})\Psi \,,$

having a structure very similar to that of the ordinary three dimensional nonrelativistic Schrödinger equation. It is a manifestly covariant equation, but at the same time its three dimensional structure is evident. The four-vectors $p_{\perp }^{\mu }$ and $x_{\perp }^{\mu }$ have only three independent components since

$P\cdot p_{\perp }=P\cdot x_{\perp }=0\,.$

The similarity to the three dimensional structure of the nonrelativistic Schrödinger equation can be made more explicit by writing the equation in the c.m. frame in which

$P=(w,{\vec {0}})$,

$p_{\perp }=(0,{\vec {p}})$,

$x_{\perp }=(0,{\vec {x}})$.

Comparison of the resultant form Template:NumBlk

with the time independent Schr\"{o}dinger equation

makes this similarity explicit.

The two-body relativistic Klein–Gordon equations

A plausible structure for the quasipotential $\Phi$ can be found by observing that the one-body Klein-Gordon equation $(p^{2}+m^{2})\psi =({\vec {p}}^{2}-\varepsilon ^{2}+m^{2})\psi =0$ takes the form $({\vec {p}}^{2}-\varepsilon ^{2}+m^{2}+2mS+S^{2}+2\varepsilon A-A^{2})\psi =0~$ when one introduces a scalar interaction and timelike vector interaction via $m\rightarrow m+S~$and $\varepsilon \rightarrow \varepsilon -A$. In the two-body case, separate classical and quantum field theory arguments show that when one includes world scalar and vector interactions then $\Phi$ depends on two underlying invariant functions $S(r)$ and $A(r)$ through the two-body Klein-Gordon-like potential form with the same general structure, that is

$\Phi =2m_{w}S+S^{2}+2\varepsilon _{w}A-A^{2}.$

Those field theories further yield the c.m. energy dependent forms

$m_{w}=m_{1}m_{2}/w,$

and

$\varepsilon _{w}=(w^{2}-m_{1}^{2}-m_{2}^{2})/2w,$

ones that Tododov introduced as the relativistic reduced mass and effective particle energy for a two-body system. Similar to what happens in the nonrelativistic two-body problem, in the relativistic case we have the motion of this effective particle taking place as if it were in an external field (here generated by $S$ and $A$). The two kinematical variables $m_{w}$ and $\varepsilon _{w}$ are related to one another by the Einstein condition

$\varepsilon _{w}^{2}-m_{w}^{2}=b^{2}(w),$

If one introduces the four-vectors, including a vector interaction $A^{\mu }$

${\mathfrak {p}}=\varepsilon _{w}{\hat {P}}+p,$

$A^{\mu }={\hat {P}}^{\mu }A(r)$

$r={\sqrt {x_{\perp }^{2}}}\,,$

and scalar interaction $S(r)$, then the following classical minimal constraint form

${\mathcal {H=}}\left({\mathfrak {p-}}A\right)^{2}+(m_{w}+S)^{2}\approx 0\,,$

reproduces Template:NumBlk Notice, that the interaction in this "reduced particle" constraint depends on two invariant scalars, $A(r)$ and $S(r)$, one guiding the time-like vector interaction and one the scalar interaction.

Is there a set of two-body Klein-Gordon equations analogous to the two-body Dirac equations? The classical relativistic constraints analogous to the quantum two-body Dirac equations (discussed in the introduction) and that have the same structure as the above Klein-Gordon one-body form are

${\mathcal {H}}_{1}=(p_{1}-A_{1})^{2}+(m_{1}+S_{1})^{2}=p_{1}^{2}+m_{1}^{2}+\Phi _{1}\approx 0$

${\mathcal {H}}_{2}=(p_{1}-A_{2})^{2}+(m_{2}+S_{2})^{2}=p_{2}^{2}+m_{2}^{2}+\Phi _{2}\approx 0,$

$p_{1}=\varepsilon _{1}{\hat {P}}+p;~~p_{2}=\varepsilon _{2}{\hat {P}}-p~.$

Defining structures that display time-like vector and scalar interactions

$\pi _{1}=p_{1}-A_{1}=[{\hat {P}}(\varepsilon _{1}-{\mathcal {A}}_{1})+p],$

$\pi _{2}=p_{2}-A_{2}=[{\hat {P}}(\varepsilon _{2}-{\mathcal {A}}_{1})-p],$

$M_{1}=m_{1}+S_{1},$

$M_{2}=m_{2}+S_{2},$

gives

${\mathcal {H}}_{1}=\pi _{1}^{2}+M_{1}^{2},$

${\mathcal {H}}_{2}=\pi _{2}^{2}+M_{2}^{2}.$

Imposing

${\begin{aligned}\Phi _{1}&=\Phi _{2}\equiv \Phi (x_{\perp })\\&=-2p_{1}\cdot A_{1}+A_{1}^{2}+2m_{1}S_{1}+S_{1}^{2}\\&=-2p_{2}\cdot A_{2}+A_{2}^{2}+2m_{2}S_{2}+S_{2}^{2}\\&=2\varepsilon _{w}A-A^{2}+2m_{w}S+S^{2},\end{aligned}}$

and using the constraint $P\cdot p\approx 0$, reproduces Eqs.(Template:EquationNote) provided

$\pi _{1}^{2}-p^{2}=-\left(\varepsilon _{1}-{\mathcal {A}}_{1}\right)^{2}=-\varepsilon _{1}^{2}+2\varepsilon _{w}A-A^{2},$

$\pi _{2}^{2}-p^{2}=-\left(\varepsilon _{2}-{\mathcal {A}}_{2}\right)^{2}=-\varepsilon _{2}^{2}+2\varepsilon _{w}A-A^{2},$

$M_{1}{}^{2}=m_{1}^{2}+2m_{w}S+S^{2},$

$M_{2}^{2}=m_{2}^{2}+2m_{w}S+S^{2}.$

The corresponding Klein-Gordon equations are

$\left(\pi _{1}^{2}+M_{1}^{2}\right)\psi =0,$

$\left(\pi _{2}^{2}+M_{2}^{2}\right)\psi =0,$

and each, due to the constraint $P\cdot p\approx 0,$ is equivalent to

${\mathcal {H\psi =}}\left(p_{\perp }^{2}+\Phi -b^{2}\right){\mathcal {\psi }}=0.$

Hyperbolic versus external field form of the two-body Dirac equations

For the two body system there are numerous covariant forms of interaction. The simplest way of looking at these is from the point of view of the gamma matrix structures of the corresponding interaction vertices of the single paraticle exchange diagrams. For scalar, pseudoscalar, vector, pseudovector, and tensor exchanges those matrix structures are respectively

$1_{1}1_{2};\gamma _{51}\gamma _{52};\gamma _{1}^{\mu }\gamma _{2\mu };\gamma _{51}\gamma _{1}^{\mu }\gamma _{52}\gamma _{2\mu };\sigma _{1\mu \nu }\sigma _{2}^{\mu \nu },$

in which

$\sigma _{i\mu \nu }={\frac {1}{2i}}[\gamma _{i\mu },\gamma _{i\nu }];i=1,2.$

The form of the Two-Body Dirac equations which most readily incorporates each or any number of these intereractions in concert is the so-called hyperbolic form of the TBDE . For combined scalar and vector interactions those forms ultimately reduce to the ones given in the first set of equations of this article. Those equations are called the external field-like forms because their appearances are individually the same as those for the usual one-body Dirac equation in the presence of external vector and scalar fields.

The most general hyperbolic form for compatible TBDE is

${\mathcal {S}}_{1}\psi =(\cosh(\Delta )\mathbf {S} _{1}+\sinh(\Delta )\mathbf {S} _{2})\psi =0\mathrm {,}$

Template:NumBlk where $\Delta$ represents any invariant interaction singly or in combination. It has a matrix structure in addition to coordinate dependence. Depending on what that matrix structure is one has either scalar, pseudoscalar, vector, pseudovector, or tensor interactions. The operators $\mathbf {S} _{1}$ and $\mathbf {S} _{2}$ are auxiliary constraints satisfying

$\mathbf {S} _{1}\psi \equiv ({\mathcal {S}}_{10}\cosh(\Delta )+{\mathcal {S}}_{20}\sinh(\Delta )~)\psi =0,$

Template:NumBlk in which the ${\mathcal {S}}_{i0}$ are the free Dirac operators Template:NumBlk This, in turn leads to the two compatibility conditions

$\lbrack {\mathcal {S}}_{1},{\mathcal {S}}_{2}]\psi =0,$

and

$\lbrack \mathbf {S} _{1},\mathbf {S} _{2}]\psi =0,$

provided that $\Delta =\Delta (x_{\perp }).$ These compatibility conditions do not restrict the gamma matrix structure of $\Delta$. That matrix structure is determined by the type of vertex-vertex structure incorporated in the interaction. For the two types of invariant interactions $\Delta$ emphasized in this article they are

$\Delta _{\mathcal {L}}(x_{\perp })=-1_{1}1_{2}{\frac {{\mathcal {L}}(x_{\perp })}{2}}{\mathcal {O}}_{1},{\text{scalar}}\mathrm {,}$

$\Delta _{\mathcal {G}}(x_{\perp })=\gamma _{1}\cdot \gamma _{2}{\frac {{\mathcal {G}}(x_{\perp })}{2}}{\mathcal {O}}_{1},{\text{vector}}\mathrm {,}$

${\mathcal {O}}_{1}=-\gamma _{51}\gamma _{52}.$

For general independent scalar and vector interactions

$\Delta (x_{\perp })=\Delta _{\mathcal {L}}+\Delta _{\mathcal {G}}.$

The vector interaction specified by the above matrix structure for an electromagnetic-like interaction would correspond to the Feynman gauge.

If one inserts Eq.(Template:EquationNote) into (Template:EquationNote) and brings the free Dirac operator (Template:EquationNote) to the right of the matrix hyperbolic functions and uses standard gamma matrix commutators and anticommutators and $\cosh ^{2}\Delta -\sinh ^{2}\Delta =1$ one arrives at $\left(\partial _{\mu }=\partial /\partial x^{\mu }\right),$

${\big (}G\gamma _{1}\cdot {\mathcal {P}}_{2}-E_{1}\beta _{1}+M_{1}-G{\frac {i}{2}}\Sigma _{2}\cdot \partial ({\mathcal {L}}\beta _{2}{\mathcal {-G}}\beta _{1})\gamma _{52}{\big )}\psi =0,$

Template:NumBlk in which

$G=\exp {\mathcal {G}},$

$\beta _{i}=-\gamma _{i}\cdot {\hat {P}},$

$\gamma _{i\perp }^{\mu }=(\eta ^{\mu \nu }+{\hat {P}}^{\mu }{\hat {P}}^{\nu })\gamma _{\nu i},$

$\Sigma _{i}=\gamma _{5i}\beta _{i}\gamma _{\perp i},$

${\mathcal {P}}_{i}\equiv p_{\perp }-{\frac {i}{2}}\Sigma _{i}\cdot \partial {\mathcal {G}}\Sigma _{i},i=1,2.$

The (covariant) structure of these equations are analogous to those of a Dirac equation for each of the two particles, with $M_{i}$ and $E_{i}$ playing the roles that $m+S$ and $\varepsilon -A$ do in the single particle Dirac equation

$(\mathbf {\gamma } \cdot \mathbf {p-} \beta (\varepsilon -A)+m+S)\psi =0.$

Over and above the usual kinetic part $\gamma _{1}\cdot p_{\perp }$ and time-like vector and scalar potential portions, the spin-dependent modifications involving $\Sigma _{i}\cdot \partial {\mathcal {G}}\Sigma _{i}$ and the last set of derivative terms are two-body recoil effects absent for the one-body Dirac equation but essential for the compatibility (consistency) of the two-body equations. The connections between what are designated as the vertex invariants ${\mathcal {L}},{\mathcal {G}}$ and the mass and energy potentials $M_{i},E_{i}$ are

$M_{1}=m_{1}\cosh {\mathcal {L}}+m_{2}\sinh {\mathcal {L}},$

$M_{2}=m_{2}\cosh {\mathcal {L}}+m_{1}\sinh {\mathcal {L}},$

$E_{1}=\varepsilon _{1}\cosh {\mathcal {G}}-\varepsilon _{2}\sinh {\mathcal {G}},$

$E_{2}=\varepsilon _{2}\cosh {\mathcal {G}}-\varepsilon _{1}\sinh {\mathcal {G}}.$

Comparing Eq.(Template:EquationNote) with the first equation of this article one finds that the spin-dependent vector interactions are

${\tilde {A}}_{1}^{\mu }={\big (}(\varepsilon _{1}-E_{1}){\big )}{\hat {P}}^{\mu }+(1-G)p_{\perp }^{\mu }-{\frac {i}{2}}\partial G\cdot \gamma _{2}\gamma _{2}^{\mu },$

$A_{2}^{\mu }={\big (}(\varepsilon _{2}-E_{2}){\big )}{\hat {P}}^{\mu }-(1-G)p_{\perp }^{\mu }+{\frac {i}{2}}\partial G\cdot \gamma _{1}\gamma _{1}^{\mu },$

Note that the first portion of the vector potentials is timelike (parallel to ${\hat {P}}^{\mu })$ while the next portion is spacelike (perpendicular to ${\hat {P}}^{\mu })$. The spin-dependent scalar potentials ${\tilde {S}}_{i}$ are

${\tilde {S}}_{1}=M_{1}-m_{1}-{\frac {i}{2}}G\gamma _{2}\cdot \partial {\mathcal {L}},$

${\tilde {S}}_{2}=M_{2}-m_{2}+{\frac {i}{2}}G\gamma _{1}\cdot {\partial }{\mathcal {L}}{.}$

The parametrization for ${\mathcal {L}}$ and ${\mathcal {G}}$ takes advantage of the Todorov effective external potential forms (as seen in the above section on the two-body Klein Gordon equations) and at the same time displays the correct static limit form for the Pauli reduction to Schrödinger-like form. The choice for these parameterizations (as with the two-body Klein Gordon equations) is closely tied to classical or quantum field theories for separate scalar and vector interactions. This amounts to working in the Feynman gauge with the simplest relation between space- and timelike parts of the vector interaction,. The mass and energy potentials are respectively

$M_{i}^{2}=m_{i}^{2}+\exp(2{\mathcal {G)(}}2m_{w}S{\mathcal {+}}S^{2}),$

$E_{i}^{2}=\exp(2{\mathcal {G(A))(}}\varepsilon _{i}-A)^{2},$

so that

$\exp({\mathcal {L}})=\exp({\mathcal {L}}(S,A))={\frac {M_{1}+M_{2}}{m_{1}+m_{2}}},$

$G=\exp {\mathcal {G=}}\exp({\mathcal {G(}}A{\mathcal {))=}}{\sqrt {\frac {1}{(1-2A/w)}}}.$

Applications and limitations

The TBDE can be readily applied to two body systems such as positronium, muonium, hydrogen-like atoms, quarkonium, and the two-nucleon system. These applications involve two particles only and do not involve creation or annihilation of particles beyond the two. They involve only elastic processes. Because of the connection between the potentials used in the TBDE and the corresponding quantum field theory, any radiative correction to the lowest order interaction can be incorporated into those potentials. To see how this comes about, consider by contrast how one computes scattering amplitudes without quantum field theory. With no quantum field theory one must come upon potentials by classical arguments or phenomenological considerations. Once one has the potential $V$ between two particles, then one can compute the scattering amplitude $T$ from the Lippmann-Schwinger equation

$T+V+VGT=0$,

in which $G$ is a Green function determined from the Schrödinger equation. Because of the similarity between the Schrödinger equation Eq. (Template:EquationNote) and the relativistic constraint equation (Template:EquationNote),one can derive the same type of equation as the above

${\mathcal {T}}+\Phi +\Phi {\mathcal {GT}}=0$,

called the quasipotential equation with a ${\mathcal {G}}$ very similar to that given in the Lippmann-Schwinger equation. The difference is that with the quasipotential equation, one starts with the scattering amplitudes ${\mathcal {T}}$ of quantum field theory, as determined from Feynman diagrams and deduces the quasipotential Φ perturbatively. Then one can use that Φ in (Template:EquationNote), to compute energy levels of two particle systems that are implied by the field theory. Constraint dynamics provides one of many, in fact an infinite number of, different types of quasipotential equations (three dimensional truncations of the Bethe-Salpeter equation) differing from one another by the choice of ${\mathcal {G}}$. The relatively simple solution to the problem of relative time and energy from the generalized mass shell constraint for two particles, has no simple extension, such as presented here with the $x_{\perp }$ variable, to either two particles in an external field or to 3 or more particles. Sazdjian has presented a receipe for this extension when the particles are confined and cannot split into clusters of a smaller number of particles with no inter-cluster interactions Lusanna has developed an approach, one that does not involve generalized mass shell constraints with no such restrictions, which extends to N bodies with or without fields. It is formulated on spacelike hypersurfaces and when restricted to the family of hyperplanes orthogonal to the total timelike momentum gives rise to a covariant intrinsic 1-time formulation (with no relative time variables) called the "rest-frame instant form" of dynamics,

See also

48 year-old Registered Nurse (Medical ) Rave from Pickering, enjoys to spend time individuals watching, new property for sale developers in singapore and cave diving. Finished a cruise liner experience that included passing by Chan Chan Archaeological Zone.

• Breit equation
• 4-vector
• Dirac equation
• Dirac equation in the algebra of physical space
• Dirac operator
• Electromagnetism
• Kinetic momentum
• Many body problem

40 year old Supply and Circulation Manager Courtney from Aberdeen, has several pursuits including bmx, property developers in new project launch singapore and actions. Finds travel a wonderful experience after visiting Central Sikhote-Alin.

• Invariant mass
• Particle physics
• Positronium
• Ricci calculus
• Special relativity
• Spin
• Quantum entanglement

Trying to invest in Singapore Actual Property , or are you attempting to promote, hire, invest, buy buy a Singapore property ? Properly then, you may have come to the fitting place in your seek for Singapore properties. Here, we are going to aid you find your dream Singapore property from our market itemizing of 1000's of Singapore properties in our Singapore real property database.

Overseas particular person who want to buy/ purchase a Restricted residential property in Sentosa Cove can acquire fast observe approval from Singapore Land Dealing Unit. Overseas particular person who want to purchase/ acquire a Restricted residential property in Sentosa Cove can apply for a long term social visit move underneath this Scheme to facilitate entry into Singapore. Foreign individual who want to apply for permanent residency in Singapore can contact SLA or MAS permitted institutions. The place you're shopping for property which is below development, the Singapore Academyof Regulation will maintain a portion of the acquisition monies as stakeholders till the expiryof the defects legal responsibility interval supplied in the Agreement/Contract. D19) Hougang / Punggol / Sengkang Condominium Common Room with Aircon

A international individual (any one who isn't a Singapore citizen, Singapore Company, Singapore restricted liability partnership or a Singapore society) will still want approval from the Singapore Land Authority (SLA) to purchase land-titled property such as houses, bungalows and vacant plots of land. Housing Improvement Board Properties SINGAPORE NON-PUBLIC RESIDENTIAL PROPERTIES Singapore firm; Singapore society. We provide invaluable services to expats who are considering relocation to Singapore For every kind of Singapore property related providers, we're there to obtain your name. You are positive to get one of the best Singapore properties with our help. RE/MAX Singapore Singapore Residential Business and Industrial Singapore citizen; Singapore Land Authority Thomson Highway, Singapore

Nevertheless, additionally it is a foul investment decision to go in too early. For instance you buy a property near one of the new MRT station location at the Thomson line. Because it takes 10 years to be accomplished, you might need difficulties renting that place out to pay off your mortgage payments. In addition, 10 years is a long time when something can occur including recession, new properties being introduced, modifications in interest rates etc. All these can have an adversarial impact on your property funding.

First, there are generally more rental transactions than gross sales transactions, to permit AV to be determined for every property based on comparable properties. Second, actions in sale costs are extra unstable than rentals. Therefore, using rental transactions to derive the AV helps to maintain property tax extra steady for property owners. If you are shopping for or trying to hire a property. It's tiring to call up individual property agent, prepare appointments, coordinate timing and to go for individual property viewing. What most individuals do is to have a property agent representing them who will organize and coordinate the viewings for all of the properties out there based mostly in your requirements & most well-liked timing. Rent Property District 12 Lease Property District thirteen

The brokers say that many Chinese language patrons are also investing abroad so they can personal property close to major instructional establishments. Some are buying houses close to top faculties — despite the fact that their youngsters are so little they can not walk but. Greater than 80 % of rich Chinese need to ship their children overseas to school, based on the Hurun Report, a Shanghai-based mostly publication. Chinese language patrons sometimes used to pick up properties within the $1 to $5 million vary in New York, typically shopping for two and three at a time for funding purposes, the brokers mentioned. Monika Tu, a dealer at high-end real estate agency Black Diamondz Property Concierge in Sydney, says that over the previous yr mainland Chinese language have develop into 80 % of her firm's business. WCEGA Plaza & Tower

An insurance coverage that covers the reinstatement worth or outstanding loan, whichever is decrease, within the event that the property search singapore (view site…) it insures is destroyed by fire. The coverage does not embody dwelling renovations, moveable household contents and personal belongings. Mortgage Insurance Credit bureau checks (e.g., Good payment data for bank cards / previous or existing loans, no previous blemishes corresponding to discharged bankrupts) A sign by the financial institution of the quantity of mortgage that you are eligible for. Nonetheless, an AIP doesn't constitute a binding loan offer. Additional checks and situations may be imposed by the financial institution, and the phrases of the formal supply will even rely upon the property that you simply intend to buy. Freehold / leasehold (999 years / 99 years)

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

• One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
  
  In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
  
  Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
  
  Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
  
  A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
  
  The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
  
  There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
• One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
  
  In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
  
  Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
  
  Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
  
  A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
  
  The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
  
  There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
• One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
  
  In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
  
  Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
  
  Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
  
  A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
  
  The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
  
  There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
• One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
  
  In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
  
  Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
  
  Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
  
  A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
  
  The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
  
  There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
• Various forms of radial equations for the Dirac two-body problem W. Królikowski (1991), Institute of theoretical physics (Warsaw, Poland)
• One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
  
  In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
  
  Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
  
  Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
  
  A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
  
  The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
  
  There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang