Fermion propagators in space-time

TL;DR

This paper analyzes fermion propagators in space-time for a non-interacting Fermi system, examining their behavior, divergences, and the effects of interactions on momentum distribution and correlations.

Contribution

It provides a detailed study of space-time dependent fermion propagators and explores how interactions and confinement influence their properties.

Findings

Propagators diverge at equal times.

Interactions modify momentum distribution and pair correlations.

Confinement effects are reflected in momentum distribution.

Abstract

The one- and the two-particle propagators for an infinite non-interacting Fermi system are studied as functions of space-time coordinates. Their behaviour at the origin and in the asymptotic region is discussed, as is their scaling in the Fermi momentum. Both propagators are shown to have a divergence at equal times. The impact of the interaction among the fermions on their momentum distribution, on their pair correlation function and, hence, on the Coulomb sum rule is explored using a phenomenological model. Finally the problem of how the confinement is reflected in the momentum distribution of the system's constituents is briefly addressed.