Electromagnetic fields in relativistic one-particle equations

In this work we reconsider magnetic-field operators in Dirac-based one-electron equations and their behaviour under unitary transformations. When approaching the non-relativistic limit within a four-component theory, the emergence of the diamagnetic contribution to second-order properties needs to be explained. This then requires to show how the magnetic-field-dependent terms that are all linear in the vector potential arrange to yield the quadratic (bilinear) term, which is the so-called diamagnetic term. An interesting suggestion by Kutzelnigg solves this problem on the operator level by invoking a unitary transformation of the electromagnetic-field-containing one-electron Dirac Hamiltonian. Naturally, this suggestion leads to the more general question of whether the vector potential needs to be incorporated into the unitary transformation that is used in transformation techniques for a decoupling of positive- and negative-energy states. We examine all different possibilities of how to transform the vector-potential-containing Dirac Hamiltonian from the perspective of the most general parametrization of unitary matrices with a special focus on the final goal to employ them in perturbative treatments of molecular property calculations.