On the non-relativistic limit of a model in quantum electrodynamics

Abstract

We consider a (semi-)relativistic spin-1/2 particle interacting with quantized radiation. The Hamiltonian has the form ${\hat{H}}_c^V:=\{c^2[(\mathbf{p}+\mathbf{A}{)}^2+\sigma \cdot \mathbf{B}]+(m{c}^2{)}^2{\}}^{1/2}-m{c}^2+V+H_f$. Assuming that the potential $|V|$ is bounded with respect to the momentum $|\mathbf{p}|$, we show that ${\hat{H}}_c^V$ converges in norm-resolvent sense to the usual Pauli-Fierz operator when $c$, the speed of light, tends to $\infty$.

13 pages