The many-body Green function of degenerate systems

TL;DR

This paper develops a rigorous non-perturbative adiabatic approximation for the evolution operator in degenerate many-body systems, resolving initial state selection issues and defining Green functions with proven convergence.

Contribution

It introduces a non-perturbative adiabatic approximation for degenerate systems and clarifies the proper initial states for Green function definitions.

Findings

Derived a non-perturbative adiabatic approximation for evolution operators.

Resolved the initial state selection problem for degenerate systems.

Established convergence of Green functions in this context.

Abstract

A rigorous non perturbative adiabatic approximation of the evolution operator in the many-body physics of degenerate systems is derived. This approximation is used to solve the long-standing problem of the choice of the initial states of H0 leading to eigenstates of H0+V for degenerate systems. These initial states are eigenstates of P0 V P0, where P0 is the projection onto a degenerate eigenspace of H0. This result is used to give the proper definition of the Green function, the statistical Green function and the non-equilibrium Green function of degenerate systems. The convergence of these Green functions is established.