  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.
