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Physical review. B./Physical review. B

Generalized Langreth rules

Lev N Kantorovich

Published Apr 6, 2020• 4 citations
Publisher

Abstract

We derive a set of rules for transforming integrals over the time contour met in the theory of nonequilibrium Green's functions (NEGF) into usual integrals over the real and imaginary times for the case when the system's Hamiltonian is different on each track. This situation is encountered, e.g., in the influence functional formalism of the path integrals theory when integrating over all trajectories associated with a part of a system.

DOI
10.1103/physrevb.101.165408

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We derive a set of rules for transforming integrals over the time contour met in the theory of nonequilibrium Green's functions (NEGF) into usual integrals over the real and imaginary times for the case when the system's Hamiltonian is different on each track. This situation is encountered, e.g., in the influence functional formalism of the path integrals theory when integrating over all trajectories associated with a part of a system.
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The nonequilibrium diagrammatics and the Dyson equations contain integrations over the time variables that run over a generic contour. In both cases, the time variables run first forward and then backward along the ordinary time axis. For computational purposes, it is then required to convert these time integrals into ordinary time integrals. To this end, it is first necessary to single out all possible combinations of the pair of time variables in the contour single-particle Green’s function. This is what is done in the present chapter.