Rational pricing: Difference between revisions

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In [[physics]], a '''kinetic term''' is the part of the [[Lagrangian]] that is [[bilinear]]{{dn|date=December 2013}} in the fields (this does not include the mass term!) (and for nonlinear sigma models, they are not even bilinear), and usually contains two [[derivative]]s with respect to time (or space); in the case of [[fermion]]s, the kinetic term usually has one derivative only. The [[equation of motion]] derived from such a Lagrangian contains differential operators which are generated by the kinetic term.


In [[mechanics]], the kinetic term is


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:<math> T = \frac{1}{2}\dot x^2 = \frac{1}{2}\left( \frac{\partial x}{\partial t}\right)^2 </math>
 
In [[quantum field theory]], the kinetic term for real [[Scalar field theory|scalar field]]s, [[electromagnetic field]] and [[Fermionic field#Dirac fields|Dirac field]] are
 
:<math> T = \frac{1}{2}\partial_\mu \Phi \partial^\mu \Phi + \frac{1}{4g^2}F_{\mu\nu}F^{\mu\nu} + i \bar \psi \gamma^\mu \partial_\mu \psi</math>
 
respectively.
 
{{DEFAULTSORT:Kinetic Term}}
[[Category:Particle physics]]
 
 
{{Physics-stub}}

Revision as of 20:52, 1 February 2014

Template:Unreferenced stub In physics, a kinetic term is the part of the Lagrangian that is bilinearTemplate:Dn in the fields (this does not include the mass term!) (and for nonlinear sigma models, they are not even bilinear), and usually contains two derivatives with respect to time (or space); in the case of fermions, the kinetic term usually has one derivative only. The equation of motion derived from such a Lagrangian contains differential operators which are generated by the kinetic term.

In mechanics, the kinetic term is

T=12x˙2=12(xt)2

In quantum field theory, the kinetic term for real scalar fields, electromagnetic field and Dirac field are

T=12μΦμΦ+14g2FμνFμν+iψ¯γμμψ

respectively.


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