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Definition of Normal Product and Wick's Theorem in Statistical Mechanics

Masanao Kitamura

Masanao Kitamura; Definition of Normal Product and Wick’s Theorem in Statistical Mechanics*), Progress of Theoretical Physics, Volume 31, Issue 6, 1 June 1964,

Progress of Theoretical PhysicsJun 1, 19640 citations

Notes on Wick's theorem in many-body theory

Luca Guido Molinari

In this pedagogical note I present the operator form of Wick's theorem, i.e. a procedure to bring a product of 1-particle creation and destruction operators to normal order, with respect to some reference many-body state. Both the static and the time-ordered cases are presented. For the latter, in particular, I provide a simple proof.

arXiv:1710.09248Oct 25, 20179 citations

Wick's theorem at finite temperature

Tim Evans, D. A. Steer

We consider Wick's Theorem for finite temperature and finite volume systems. Working at an operator level with a path ordered approach, we show that contrary to claims in the literature, expectation values of normal ordered products can be chosen to be zero and that results obtained are independent of volume. Thus the path integral and operator approaches to finite temperature and finite volume quantum field theories are indeed seen to be identical. The conditions under which normal ordered products have simple symmetry properties are also considered.We consider Wick's Theorem for finite temperature and finite volume systems. Working at an operator level with a path ordered approach, we show that contrary to claims in the literature, expectation values of normal ordered products can be chosen to be zero and that results obtained are independent of volume. Thus the path integral and operator approaches to finite temperature and finite volume quantum field theories are indeed seen to be identical. The conditions under which normal ordered products have simple symmetry properties are also considered.

Jan 1, 199621 citations

Extension of Wick’s theorem by means of the state operator formalism

Masao Nomura

Reordering of operators in the second quantization formalism is described by using state operators as basic operators, where the state operator is either a cluster of creation operators or that of annihilation operators specified by a set of quantum numbers of any representation. The commutation relation between state operators is simply expressed in terms of the coefficient of fractional parentage (cfp), the factor specific to state operator (de) composition. Wick’s theorem, prevalently applied to a string of creation and annihilation operators, is extended to a string of state operators. Similar extension is done for the contraction theorem.Reordering of operators in the second quantization formalism is described by using state operators as basic operators, where the state operator is either a cluster of creation operators or that of annihilation operators specified by a set of quantum numbers of any representation. The commutation relation between state operators is simply expressed in terms of the coefficient of fractional parentage (cfp), the factor specific to state operator (de) composition. Wick’s theorem, prevalently applied to a string of creation and annihilation operators, is extended to a string of state operators. Similar extension is done for the contraction theorem.

Journal of Mathematical PhysicsApr 1, 198514 citations

Application of some algebraic arguments to the theory of normal Fermi systems

А. А. Повзнер

Theoretical and Mathematical PhysicsJan 1, 19732 citations

A proof of Wick's theorem for spin operators

Jenő Sólyom

Physics Letters ANov 1, 19681 citation

Extension of the Notion of Normal Products and Wick's Theorem to Finite Temperature

Abstract

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Extension of the Notion of Normal Products and Wick's Theorem to Finite Temperature

Abstract

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