Derivative four-fermion model, effective action and bumblebee generation

TL;DR

This paper analyzes a derivative four-fermion model, demonstrating the radiative generation of a bumblebee-like potential, exploring phase transitions at finite temperature, and deriving the low-energy effective action with Lorentz symmetry considerations.

Contribution

It provides a detailed study of the effective potential and phase transitions in a derivative four-fermion model, including finite temperature effects and the derivation of the low-energy effective action.

Findings

A bumblebee-like potential is radiatively generated.

Finite temperature induces phase transitions restoring Lorentz symmetry.

The low-energy effective action includes a kinetic term and a bumblebee potential.

Abstract

In this paper, we study the one-loop effective potential of a derivative four-fermion model. As a result, an exact bumblebee-like potential is radiatively generated. Afterwards, we generalize our study for a finite temperature case and explicitly demonstrate the possibility of phase transitions allowing for the restoration of the Lorentz symmetry. We also investigate the low-energy effective action, from which we obtain the usual kinetic term and the corresponding bumblebee potential.