Non-Abelian fields in very special relativity

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 ${n}_{\ensuremath{\mu}}$, 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 Becchi-Rouet-Stora-Tyutin formalism to fix the gauge. The model is renormalizable and unitary and for non-Abelian groups, asymptotically free.