  We consider a (semi-)relativistic spin-1/2 particle interacting with
quantized radiation. The Hamiltonian has the form
$\hat{H}_c^V:=\{c^2[(\mathbf{p}+{\bf A})^2+{\bf \sigma}\cdot{\bf
B}]+(mc^2)^2\}^{1/2}-mc^2+V+H_f$. 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 $\infty$.
