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Zhur. Eksptl'. i Teoret. Fiz.

ON THE ANALYTICAL PROPERTIES OF THE SINGLE-FERMION GREEN'S FUNCTION IN QUANTUM THEORY OF MANY PARTICLES

Sergei V. Maleev

Published Nov 1, 1961• 0 citations
OpenAlex

Abstract

The analytical properties of the single-fermion Green's function and the mass operator in quantum theory of many particles are investigated. In particular, the poles of the mass operator are studied. (auth)

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arXiv:cond-mat/9710343•Physical review. B, Condensed matter•Aug 15, 1998•7 citations
In this paper we discuss some general properties of the one-particle Green's function, for nonuniform many-fermion systems and the associated single-particle interpretation of physical properties of such systems. We consider, in particular, the ground-state energy, the density of particles in the ground state, and the single-particle excitation spectrum. The investigation is restricted to the case of a static external field and a system at zero temperature. Various general approximation methods are studied starting from one in which the self-energy operator is replaced by an Hermitian and energy-independent operator.
Some analytic properties of the single-particle Green functions and proper self-energy parts for a system of interacting bosons at nonzero temperatures are derived. In particular, it is shown how to obtain the analytical continuations of simple functions of the proper self-energy parts, which can be obtained from perturbation theory at an infinite set of points along the imaginary energy axis, to the whole of the complex energy plane. This is useful in determining the poles of the Green functions.
A simple model of noninteracting electrons with a separable one-body potential is used to discuss the possible pole structure of single-particle Green's functions for fermions on unphysical sheets in the complex frequency plane as a function of the system parameters. The poles in the exact Green's function can cross the imaginary axis, in contrast to recent claims that such a behavior is unphysical. As the Green's function of the model has the same functional form as an approximate Green's function for coupled Luttinger liquids, no definite conclusions concerning the concept of ``confined coherence'' can be drawn from the locations of the poles of this Green's function.