Fermion Self-energy and Pseudovector Condensate in NJL Model with External Magnetic Field

TL;DR

This paper investigates the complete fermion self-energy in the NJL model under external magnetic fields, revealing new phases and the role of pseudovector condensates in chiral symmetry breaking and particle dispersion.

Contribution

It introduces a comprehensive form of self-energy including four condensates, proposes a new quasi-Wigner phase, and analyzes the effects of pseudovector condensates on particle properties.

Findings

Identification of a new quasi-Wigner phase with partial chiral symmetry restoration.

Demonstration that pseudovector condensates cause energy level splitting.

Modification of dynamical mass and phase transition behavior under magnetic fields.

Abstract

In this paper, we aim to study the complete self-energy in the fermion propagator within two-flavor NJL model in the case of finite temperature, chemical potential and external magnetic field. Through Fierz transformation we prove that the self-energy is not simply proportional to dynamical mass in the presence of chemical potential, moreover, it contains four kinds of condensates after introducing external magnetic field. We find out the appropriate and complete form of self-energy and establish new gap equations. We take two of the four condensates (scalar and pseudovector condensates) to make an approximation and simplify the gap equations. The numerical results show that not only the dynamical mass get quantitative modification, but also the properties of Nambu phase and Wigner phase are significantly different with classic results. Instead of classic Wigner phase with zero dynamic mass in the massless NJL model, we propose a new phase - quasi-Wigner phase in this article, it has small but nonzero dynamic mass, with increasing chemical potential, eventually Nambu phase will turn into quasi-Wigner phase with first-order phase transition, therefore the chiral symmetry can never be fully restored but be partially restored. Furthermore, we prove that pseudovector condensate in self-energy can generate energy splitting in dispersion relation, it will cause minor differences of particle numbers with the split energy levels.