A Lorentz-violating SO(3) model: discussing the unitarity, causality and the 't Hooft-Polyakov monopoles

TL;DR

This paper extends Lorentz-violating quantum electrodynamics to an SO(3) non-Abelian model, analyzing unitarity, causality, and monopole solutions, revealing the persistence of 't Hooft-Polyakov monopoles despite Lorentz violation.

Contribution

It introduces a Lorentz-violating non-Abelian SO(3) model with a Chern-Simons term and examines its spectrum, unitarity, causality, and topological monopole solutions.

Findings

Monopole solutions remain present despite Lorentz violation.

Unitarity and causality are analyzed within the extended model.

The topological structure supports 't Hooft-Polyakov monopoles.

Abstract

In this paper, we extend the analysis of the Lorentz-violating Quantum Eletrodynamics to the non-Abelian case: an SO(3) Yang-Mills Lagrangian with the addition of the non-Abelian Chern-Simons-type term. We consider the spontaneous symmetry breaking of the model and inspect its spectrum in order to check if unitarity and causality are respected. An analysis of the topological structure is also carried out and we show that a 't Hooft-Polyakov solution for monopoles is still present.