NON-RELATIVISTIC LIMIT OF A DIRAC–MAXWELL OPERATOR IN RELATIVISTIC QUANTUM ELECTRODYNAMICS

Abstract

The non-relativistic (scaling) limit of a particle-field Hamiltonian H, called a Dirac–Maxwell operator, in relativistic quantum electrodynamics is considered. It is proven that the non-relativistic limit of H yields a self-adjoint extension of the Pauli–Fierz Hamiltonian with spin 1/2 in non-relativistic quantum electrodynamics. This is done by establishing in an abstract framework a general limit theorem on a family of self-adjoint operators partially formed out of strongly anticommuting self-adjoint operators and then by applying it to H.