The superradiant phase transition was the subject of a wide discussion as to whether or not it is only a result of the simplified model of the matter-field interaction; and if it can occur for the real physical parameters of physical systems (a no-go theorem). However, both the original derivation and the later corrections leading to nonexistence of the transition – due to Thomas–Reiche–Kuhn sum rule canceling for the harmonic oscillator the needed inequality to impossible negativity of the interaction – were based on the assumption that the quantum field operators are commuting numbers, and the atoms do not interact with the static Coulomb forces. This is generally not true like in case of Bohr–van Leeuwen theorem and the classical non-existence of Landau diamagnetism. The negating results were also the consequence of using the simple Quantum Optics models of the electromagnetic field-matter interaction but not the more realistic Condenced Matter models like for example the superconductivity model of the BCS but with the phonons replaced by photons to first obtain the collective polaritons. The return of the transition basically occurs because the inter-atom dipole-dipole or generally the electron-electron Coulomb interactions are never negligible in the condensed and even more in the superradiant matter density regime and the Power-Zienau unitary transformation eliminating the quantum vector potential in the minimum-coupling Hamiltonian transforms the Hamiltonian exactly to the form used when it was discovered and without the square of the vector potential which was later claimed to prevent it. Alternatively within the full quantum mechanics including the electromagnetic field the generalized Bohr–van Leeuwen theorem does not work and the electromagnetic interactions cannot be eliminated while they only change the p ⋅ ⋅ A vector potential coupling to the electric field x ⋅ ⋅ E coupling and alter the effective electrostatic interactions. It can be observed in model systems like Bose–Einstein condensates and artificial atoms.