Non Abelian Fields in Very Special Relativity

TL;DR

This paper explores non-Abelian gauge fields within Very Special Relativity, demonstrating their mass generation, algebraic structure, and quantization, with implications for particle physics models.

Contribution

It introduces a consistent framework for non-Abelian fields in VSR, including gauge transformations, matter couplings, and quantization, extending previous Abelian results.

Findings

Gauge fields become massive in VSR.

VSR gauge transformations form a closed algebra.

Model is renormalizable, unitary, and asymptotically free for non-Abelian groups.

Abstract

We study non-Abelian fields in the context of very special relativity (VSR). For this we define the covariant derivative and the gauge field gauge transformations, both of them involving a fixed null vector $n_{\mu}$, related to the VSR breaking of the Lorentz group to the Hom(2) or Sim(2) subgroups. As in the Abelian case the gauge field becomes massive. Moreover we show that the VSR gauge transformations form a closed algebra. We then write actions coupling the gauge field to various matter fields (bosonic and fermionic). We mention how we can use the spontaneous symmetry breaking mechanism to give a flavor dependent VSR mass to the gauge bosons. Finally, we quantize the model using the BRST formalism to fix the gauge. The model is renormalizable and unitary and for non abelian groups, asymptotically free.