Interaction of Schrödinger electrons and photons

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Abstract
The effect of transformations carried out on the Hamiltonian for the Schrödinger electron-photon system is studied. These transformations include gauge transformations and certain similarity and "hybrid" transformations. The last named involve unitary transformations of either operators or states, but not both. Unitary and hybrid transformation are discussed, which affect the transverse components of the electromagnetic vector potentials and therefore are distinct from gauge transformations. A hybrid transformation is identified which leads to a form of the Hamiltonian that contains no reference to the transverse vector potential and includes electric and magnetic fields as well as nonlocal interactions of charges and currents. The behavior of the scattering matrix under the influence of these hybrid transformations is discussed. Comments are made on two-photon absorption calculations.