Theory of photon condensation in an arbitrary-gauge condensed matter cavity model

We derive an arbitrary-gauge criterion under which condensed matter within electromagnetic field may transition to a photon phase. Previous results are recovered by selecting the Coulomb gauge wherein condensation can only occur for spatially varying and be interpreted as magnetic instability. demonstrate invariance of our description directly, but since photons gauge-relative concepts we find more generally that uniform relative extent instability is both electric versus purely or depends on gauge. use propose method detect