Arbitrary gauge quantisation of light-matter theories with time-dependent constraints

Abstract: We provide a general framework for the quantisation of light-matter theories with time-dependent holonomic constraints. Unless time dependence is present from the outset at the Lagrangian level, different gauges generally produce non-equivalent canonical theories. The irrotational gauge is defined as that which also yields a correct theory when time dependence is introduced at the Hamiltonian level. We unify examples of such gauges found in existing literature. In particular, we show that for describing time-dependent light-matter interactions the Coulomb gauge is not generally irrotational, so it does not enjoy any special status, contradicting the conclusions in Phys. Rev. A 107, 013722 (2023) and Phys. Rev. Research 3, 023079 (2021), while reaffirming the prior treatment and conclusions reported in Phys. Rev. Research 3, 013116 (2021).