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Physical Review A

Perturbation expansion of closed-time-path Green’s functions

Hong-Hua Xu, Chien-hua Tsai

Published Jan 1, 1990• 11 citations
Publisher

Abstract

The incoming interaction picture is introduced in accordance with the adiabatic hypothesis. A generalized Wick's theorem and, accordingly, a real-time formalism of perturbation theory at finite temperatures are constructed for the closed-time-path Green's functions. This new approach is illustrated in terms of the simple case of an electron-phonon system.

DOI
10.1103/physreva.41.53

Related papers

On the Perturbation Expansion of Closed Time Path Green's Functions

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The incoming interaction picture is introduced in accordance with the adiabatic hypothesis. A generalized Wick's theorem and, accordingly, a real time formalism of perturbation theory at finite temperatures are constructed for the closed Time Path Green's Functions (CTPGF). This new approach is illustrated in terms of the simple case of an electron-phonon system.

Communications in Theoretical Physics•Jan 1, 1990•0 citations

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This chapter considers a general form of the Wick’s theorem, which leads to a perturbation expansion of the (contour) single- and two-particle Green’s functions, which are expressed in terms of the contour time-ordering operator. The strategy for proving the Wick’s theorem is similar to that adopted within the Matsubara formalism for the Green’s functions at finite temperature and relies on the Gibbs form of the statistical operator in the interaction picture. An extension to superfluid Bose and Fermi systems is also considered.

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Comment on "Perturbation expansion of closed-time-path Green's functions"

Stéphane Vago, T. Toutain

The "incoming" interaction picture found by Xu and Tsai [Phys. Rev. A 41, 53 (1990)], used to develop a convenient formulation of the closed-time-path approach to Green's function theory, is shown to be a particular case of a more general set of solutions.

Physical Review A•Oct 1, 1995•2 citations

Non-equilibrium Green functions: generalized Wick's theorem and diagrammatic perturbation with initial correlations

A.G. Hall

Wick's theorem is combined with a cluster composition to derive a generalized statistical Wick's theorem for a non-equilibrium system with initial correlations. This enables a diagrammatic time-dependent perturbation theory which is a simple extension of the usual one to be developed for time-path causal statistical Green functions and their matrix equivalents. This provides a complete non-equilibrium theory. Reduction of diagrams and equations of motion for the Green functions are also discussed.

Journal of Physics A Mathematical and General•Feb 1, 1975•72 citations

Reply to "Comment on `Perturbation expansion of closed-time-path Green's functions' "

Hong-Hua Xu

Controversial points in this Comment concerning the general picture transformations which may give rise to a variety of interaction pictures are analyzed.Received 26 April 1995DOI:https://doi.org/10.1103/PhysRevA.52.3379©1995 American Physical Society

Physical Review A•Oct 1, 1995•0 citations

Green functions for strongly correlated electronic systems

Canio Noce

By means of the path-integral formalism, a general procedure for the evaluation of the exact n-point Green functions at finite temperature is developed for the analysis of strongly correlated electron systems. The densities of states for two different types of electrons are written by using a non-standard perturbation expansion.

Journal of Physics Condensed Matter•Oct 7, 1991•5 citations
The incoming interaction picture is introduced in accordance with the adiabatic hypothesis. A generalized Wick's theorem and, accordingly, a real-time formalism of perturbation theory at finite temperatures are constructed for the closed-time-path Green's functions. This new approach is illustrated in terms of the simple case of an electron-phonon system.
This chapter considers a general form of the Wick’s theorem, which leads to a perturbation expansion of the (contour) single- and two-particle Green’s functions, which are expressed in terms of the contour time-ordering operator. The strategy for proving the Wick’s theorem is similar to that adopted within the Matsubara formalism for the Green’s functions at finite temperature and relies on the Gibbs form of the statistical operator in the interaction picture. An extension to superfluid Bose and Fermi systems is also considered.
Wick's theorem is combined with a cluster composition to derive a generalized statistical Wick's theorem for a non-equilibrium system with initial correlations. This enables a diagrammatic time-dependent perturbation theory which is a simple extension of the usual one to be developed for time-path causal statistical Green functions and their matrix equivalents. This provides a complete non-equilibrium theory. Reduction of diagrams and equations of motion for the Green functions are also discussed.