Gauge Theories with Lorentz-Symmetry Violation by Symplectic Projector Method

TL;DR

This paper analyzes Lorentz-symmetry violation in gauge theories using the Symplectic Projector Method, confirming stability for space-like vectors and tachyonic modes for time-like vectors within the Carroll-Field-Jackiw model.

Contribution

It applies the Symplectic Projector Method to study Lorentz violation, providing a canonical formulation and confirming stability and instability conditions for different vector configurations.

Findings

Space-like $v^{}$ vectors are stable.

Time-like $v^{}$ vectors exhibit tachyonic modes.

Dispersion relations align with recent literature.

Abstract

The violation of Lorentz symmetry is studied from the point of view of a canonical formulation. We make the usual analysis on the constraints structure of the Carroll-Field-Jackiw model. In this context we derive the equations of motion for the physical variables and check out the dispersion relations obtained from them. Therefore, by the analysis using Symplectic Projector Method (SPM), we can check the results about this type of Lorentz breaking with those in the recent literature: in this sense we can confirm that the configuration of $v^{\mu}$ space-like is stable, and the $v^{\mu}$ time-like carry tachionic modes.