Gauge Invariant Truncated Models in Cavity Quantum Electrodynamics

Resolving gauge ambiguities for truncated matter models coupled to quantum light has received a lot of attention recently. Equivalence of the dipole gauge and the coulomb gauge Hamiltonians was achieved by properly constructing unitary operators in the truncated matter subspace. We revisit these ideas and discuss gauge invariance in a general setting, not necessarily restricted to the dipole or the coulomb gauges.