Spectral properties of four-time fermionic Green's functions

TL;DR

This paper derives spectral relations for four-time fermionic Green's functions, clarifies zero-frequency anomalies, and provides high-frequency expansions, advancing theoretical understanding of complex quantum many-body systems.

Contribution

It introduces the most general spectral relations for four-time fermionic Green's functions and elucidates zero-frequency anomalies related to second cumulants.

Findings

Separated zero-frequency anomaly terms and linked them to second cumulants.

Derived high-frequency expansions in different frequency space directions.

Extended spectral relation framework to the most general case.

Abstract

The spectral relations for the four-time fermionic Green's functions are derived in the most general case. The terms which correspond to the zero-frequency anomalies, known before only for the bosonic Green's functions, are separated and their connection with the second cumulants of the Boltzmann distribution function is elucidated. The high-frequency expansions of the four-time fermionic Green's functions are provided for different directions in the frequency space.