Thermal nonlocal Nambu--Jona-Lasinio model in the real time formalism

TL;DR

This paper develops a real-time finite temperature formalism for the nonlocal Nambu--Jona-Lasinio model, revealing quasiparticle behavior, confinement signals, and decay widths through spectral functions and complex poles.

Contribution

It introduces a comprehensive real-time thermal propagator for the nonlocal NJL model with a Gaussian regulator, including complex poles as confinement indicators.

Findings

Propagation of massive quasiparticles at finite temperature

Complex poles indicating confinement signals

Expression for propagator along the critical line

Abstract

The real-time formalism at finite temperature and chemical potential for the nonlocal Nambu--Jona-Lasinio model is developed in the presence of a Gaussian covariant regulator. We construct the most general thermal propagator, by means of the spectral function. As a result, the model involves the propagation of massive quasiparticles. The appearance of complex poles is interpreted as a confinement signal, and in this case we have unstable quasiparticles with a finite decay width. An expression for the propagator along the critical line, where complex poles start to appear, is also obtained. A generalization to other covariant regulators is proposed.