  We generalize the Power-Zineau-Woolley transformation to obtain a canonical
Hamiltonian of cavity quantum electrodynamics for arbitrary geometry of
boundaries. This Hamiltonian is free from the A-square term and the
instantaneous Coulomb interaction between distinct atoms. The single-mode
models of cavity QED (Dicke, Tavis-Cummings, Jaynes-Cummings) are justified by
a term by term mapping to the proposed microscopic Hamiltonian. As one
straightforward consequence, the basis of no-go argumentations concerning the
Dicke phase transition with atoms in electromagnetic fields dissolves.
