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ON THE USE OF GREEN FUNCTIONS IN PERTURBATION THEORY. PART II

D. Ter Haar, Harald Wergeland

Published Jan 1, 1961• 0 citations
OpenAlex

Abstract

A Green's function method is used to calculate the natural line width of a spectral line of a many-body system. The result is shown to be identical to the result obtained by time-dependent perturbation theory. (T.F.H.)

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Despite its centrality in the mathematical structure of perturbative many-body theory, the total Green's function for the many-body time-dependent Schrodinger equation has been ignored for decades, superseded by single-particle Green's functions, for which a vast portion of the literature has been devoted. In this paper, we give the first computation the total Green's function for the time-dependent Schrodinger equation for a non-interacting system of identical particles, setting the stage for a fresh interpretation of perturbative many-body physics.
The Green’s function method in the Kadanoff-Baym version provides a basic theory for nuclear dynamics which is applicable also to nonzero temperature and to nonequilibrium systems. At the same time, it maintains the basic many-body techniques of the Brueckner theory that makes reasonable a comparison of the numerical results of the two methods for equilibrium systems. The correct approximation to the spectral function which takes into account the widths of energy levels is offered and discussed, and the comparison of the values of binding energy in the two methods is produced.