Dyson-Schwinger equation approach to Lorentz Symmetry Breaking with finite temperature and chemical potential

TL;DR

This paper explores how Lorentz symmetry can be dynamically broken in a fermionic system at finite temperature and chemical potential using Dyson-Schwinger equations, revealing phase transitions and critical parameters.

Contribution

It introduces a nonperturbative Dyson-Schwinger framework incorporating temperature and chemical potential to study Lorentz symmetry breaking.

Findings

Lorentz symmetry breaking occurs in the strong coupling regime.

Phase diagrams depend on temperature and chemical potential.

Critical temperature and chemical potential vary with coupling strength.

Abstract

In this work, we investigate the dynamical breakdown of Lorentz symmetry in 4 dimensions by the condensation of a fermionic field described by a Dirac Lagrangian with a four-fermion interaction. Using the Keldysh formalism we show that the Lorentz symmetry breaking modifies the Dyson-Schwinger equations of the fermionic propagator. We analyze the nonperturbative solutions for the Dyson-Schwinger equations using the combination of the rainbow and quenched approximations and show that, in equilibrium, the Lorentz symmetry breakdown can occur in the strong coupling regime and new features arise from this approach. Finally, we analyze the contributions of temperature and chemical potential and find the respective phase diagram of the model and analyze the dependence of the critical temperature and chemical potential as functions of the coupling constant.