Gauge Invariant QED with Arbitrary Mixing of p · A and q · E Interactions

Abstract

The minimal-coupling Hamiltonian for a non-relativistic bound system of two charges in the dipole approximation is gauge transformed to a Hamiltonian of a variable gauge which mixes the usual p · A and q · E interactions, and re-scales the charges. Various photon transition processes—single photon absorption and emission; two-photon scattering and absorption; the Lamb shift—are investigated by perturbation theory and found to be gauge independent, providing the transitions occur on the energy shell. It is demonstrated how a particular choice of gauge removes the counter-rotating terms and diagonalises the Hamiltonian of a coupled oscillator and two-level atom.