Out-of-equilibrium chiral and $U_A(1)$ symmetry breaking in electromagnetic fields

TL;DR

This paper investigates how external electromagnetic fields influence chiral and $U_A(1)$ symmetry breaking in quark matter, revealing quantum effects and off-shell phenomena using a Wigner function approach.

Contribution

It provides a systematic quantum analysis of symmetry breaking under electromagnetic fields within the NJL model, highlighting quantum-level $U_A(1)$ breaking and off-shell effects.

Findings

Chiral symmetry is broken at the classical level.

$U_A(1)$ symmetry breaking occurs only at the quantum level.

Off-shell effects cause oscillations in condensates.

Abstract

We systematically study quantum effect on chiral and $U_A(1)$ symmetry breaking under external electromagnetic fields in the frame of equal-time Wigner function formalism. We derive the transport and constraint equations for the quark distribution functions and the chiral and pion condensates in a Nambu--Jona-Lasinio model. By taking semi-classical expansion of the equations, chiral symmetry is broken at classical level, while $U_A(1)$ symmetry breaking happens only at quantum level. Beyond quasi-particle approximation, the quark off-shell effect leads to strong oscillation for the chiral and pion condensates.