Carrollian Yang-Mills theories in the homogeneous temporal gauge

Abstract

We quantize, in the homogeneous temporal gauge, both the electric and the magnetic Carrollian Yang-Mills theories with SU(N) gauge symmetry in the fundamental representation. We use the BRST method implemented in the path integral. We show that in the first case all the interaction vertices vanish, thus, giving a free theory. In the magnetic case, there are no loop contributions to the Green functions of the elementary fields --i.e., Green functions not involving composite operators-- and the only connected parts of such Green functions with a dependence on the coupling constant are the tree level contributions to the three and four point functions of the field $ξ_i$. We also show that in the magnetic case the Green functions involving only Wilson loops are trivial and not so in the electric case.