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The long-standing debate whether the phase transition in the Dicke model canbe realized with dipoles in electromagnetic fields is yet an unsettled one. Thewell-known statement often referred to as the "no-go theorem", asserts that theso-called A-square term, just in the vicinity of the critical point, becomesrelevant enough to prevent the system from undergoing a phase transition. Atvariance with this common belief, in this paper we prove that the Dicke modeldoes give a consistent description of the interaction of light field with theinternal excitation of atoms, but in the dipole gauge of quantumelectrodynamics. The phase transition cannot be excluded by principle and aspontaneous transverse-electric mean field may appear. We point out that thesingle-mode approximation is crucial: the proper treatment has to be based oncavity QED, wherefore we present a systematic derivation of the dipole gaugeinside a perfect Fabry-P\'erot cavity from first principles. Besides the impacton the debate around the Dicke phase transition, such a cleanup of thetheoretical ground of cavity QED is important because currently there are manyemerging experimental approaches to reach strong or even ultrastrong couplingbetween dipoles and photons, which demand a correct treatment of the Dickemodel parameters.

Adequacy of the Dicke model in cavity QED: a counter-"no-go" statement