Towards Carrollian quantization: renormalization of Carrollian electrodynamics

Field-theoretic description of Carrollian theories has largely remained classical so far. In this paper, we attempt to study the renormalization of Carrollian gauge field theories via path integral techniques. The case of Carrollian electrodynamics minimally coupled to a massive Carrollian scalar is considered. We report potential problems such as IR divergences and mass shell singularity cropping up at the first order in the perturbation. Perhaps, the most important result that we report is how conventional arguments for gauge independence for mass and coupling are invalidated for a gauge theory in a Carrollian setting. As of now, the renormalization of Carrollian gauge field theories seems to suffer from unphysical ramifications. Possible cures to resolve these issues are suggested.