The structure of Green functions in quantum field theory with a general state

TL;DR

This paper develops a method to analyze Green functions in quantum field theory for general states, extending beyond the vacuum case, and derives nonperturbative equations by transforming cumulants into interaction terms.

Contribution

It introduces a novel approach to determine the structure of Green functions for arbitrary states and derives nonperturbative equations using cumulant transformations.

Findings

Method to analyze Green functions in general states

Derivation of nonperturbative equations for these Green functions

Framework applicable to degenerate systems and complex states

Abstract

In quantum field theory, the Green function is usually calculated as the expectation value of the time-ordered product of fields over the vacuum. In some cases, especially in degenerate systems, expectation values over general states are required. The corresponding Green functions are essentially more complex than in the vacuum, because they cannot be written in terms of standard Feynman diagrams. Here, a method is proposed to determine the structure of these Green functions and to derive nonperturbative equations for them. The main idea is to transform the cumulants describing correlations into interaction terms.