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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]].
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| 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.
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| 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.
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| ==Example: Scalar Field==
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| 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
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| <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>
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| In the Schrödinger representation this functional generates time translations of state wave functionals, via
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| <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>.
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| ==Further reading==
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| * Brian Hatfield, ''Quantum Field Theory of Point Particles and Strings''. Addison Wesley Longman, 1992. See Chapter 10 "Free Fields in the Schrodinger Representation".
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| * 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.
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| * 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).
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| * 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.
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| * 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.
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| {{DEFAULTSORT:Schrodinger Functional}}
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| [[Category:Quantum field theory]]
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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.
Stop by my web site; std testing at home