en>Nurg: /* Technical details */ sp.

2014-08-05T07:22:22Z

Technical details: sp.

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	~~{{Unreferenced\|date=December 2009}}~~		Hello and welcome. My name is Figures Wunder. To perform baseball is the hobby he will never stop performing. Bookkeeping is my occupation. Her family life in Minnesota.<br><br>Stop by my web site; [http://www.ninfeta.tv/blog/99493 std testing at home]
	~~Some approaches to [[quantum field theory]] are more popular than others~~. ~~For historical reasons the [[Schrodinger picture\|Schrödinger representation]]~~ is ~~less favoured than [[Fock space]] methods~~. ~~In the early days of [[quantum field theory]] maintaining symmetries such as Lorentz invariance and proving renormalisation were of paramount importance. The Schrödinger representation~~ is ~~not manifestly Lorentz invariant and its renormalisability was only shown as recently as~~ the ~~1980s by [[Kurt Symanzik]]~~.

	~~Within the Schrödinger representation the Schrödinger functional stands out as perhaps the most useful and versatile functional tool, though interest in it~~ is ~~shown only by a few researchers~~.

	~~The Schrödinger functional is not itself [[nature\|physical]]. It is,~~ in its most basic form, the time translation generator of state wavefunctionals. In layman's terms, it defines how a system of [[quantum]] particles evolves through time and what the later systems may look like.

	~~==Example: Scalar Field==~~
	~~The basic mathematical definition is as follows~~. ~~In the [[quantum field theory]] of (as example) a [[scalar field]]~~ <~~math~~>~~\phi~~<~~/math~~> ~~with a time independent Hamiltonian <math>H</math> the Schrödinger functional is defined as~~

	~~<math>\mathcal{S}[\phi_2,t_2;\phi_1,t_1]=\langle\,\phi_2\,\|e^{-iH(t_2-t_1)/\hbar}\|\,\phi_1\,\rangle.</math>~~

	~~In the Schrödinger representation this functional generates time translations of state wave functionals, via~~
	~~<math>\Psi[\phi_2,t_2] = \int\!\mathcal{D}\phi_1\,\,\mathcal{S}[\phi_2,t_2;\phi_1,t_1]\Psi[\phi_1,t_1]</math>.~~

	~~==Further reading==~~
	* Brian Hatfield, ''Quantum Field Theory of Point Particles and Strings''. Addison Wesley Longman, 1992. See Chapter 10 "Free Fields in the Schrodinger Representation".
	* I.V. Kanatchikov, "Precanonical Quantization and the Schroedinger Wave Functional." ''Phys.Lett. A'' '''283''' (2001) 25–~~36. Eprint [http://arxiv.org/abs/hep-th/0012084 arXiv:hep-th/0012084], 16 pages.~~
	* R. Jackiw, "Schrodinger Picture for Boson and Fermion Quantum Field Theories." In ''Mathematical Quantum Field Theory and Related Topics: Proceedings of the 1987 Montréal Conference Held September 1–5, 1987'' (eds. J.S. Feldman and L.M. Rosen, American Mathematical Society 1988).
	* H. Reinhardt, C. Feuchter, "On the Yang-Mills wave functional in Coulomb gauge." ''Phys.Rev. D'' '''71''' (2005) 105002. Eprint [http://~~arxiv~~.~~org/abs/hep-th/0408237 arXiv:hep-th/0408237], 9 pages~~.
	* D.V. Long, G.M. Shore, "The Schrodinger Wave Functional and Vacuum States in Curved Spacetime." ''Nucl.Phys. B'' '''530''' (1998) 247–278. Eprint [http://arxiv.org/~~abs~~/~~hep-th/9605004 arXiv:hep-th/9605004], 41 pages.~~

	~~{{DEFAULTSORT:Schrodinger Functional}}~~
	~~[[Category:Quantum field theory]~~]

en>Polytope24 at 02:51, 5 September 2013

2013-09-05T02:51:56Z

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en>Nurg: /* Technical details */ sp.

en>Polytope24 at 02:51, 5 September 2013

70.247.165.249: avoid redirect