Diamagnetism in relativistic theory

Abstract

A unitary transformation of the Dirac operator in a magnetic field is presented, which leads to a reformulation of the interaction of a Dirac particle with a magnetic field, in which, as in nonrelativistic theory, diamagnetic and paramagnetic contributions appear naturally, but at a four-component-spinor level. The diamagnetic contribution to the magnetic susceptibility consists of two terms, each of which is evaluated as a simple expectation value with the unperturbed relativistic wave function. One of the two terms closely resembles its nonrelativistic counterpart. The proposed formalism is analyzed in the context of the direct perturbation theory of relativistic effects. It is compared with the more traditional sum-over-states approach including negative-energy states, as well as with a Fock-space formulation. In the latter, the vacuum energy depends on the external magnetic field. The creation of a particle (electron or positron) is accompanied by a change of the vacuum energy via a kind of exclusion effect. This change can be identified with the diamagnetism of the particle. The access to diamagnetism and paramagnetism based on the Gordon decomposition of the induced current density is to some extent, but not entirely, equivalent to that which results from the unitary transformation. For a physically meaningfulmore » decomposition of the current density a combination of the Gordon approach with the unitary transformation is recommended. Neither the interpretation nor the computation of diamagnetic contributions in terms of negative-energy states is encouraged.« less