  We consider an electron coupled to the quantized radiation field and subject
to a slowly varying electrostatic potential. We establish that over
sufficiently long times radiation effects are negligible and the dressed
electron is governed by an effective one-particle Hamiltonian. In the proof
only a few generic properties of the full Pauli-Fierz Hamiltonian H_PF enter.
Most importantly, H_PF must have an isolated ground state band for |p| < p_c <=
\infty with p the total momentum and p_c indicating that the ground state band
may terminate. This structure demands a local approximation theorem, in the
sense that the one- particle approximation holds until the semi-classical
dynamics violates |p|<p_c. Within this framework we prove an abstract Hilbert
space theorem which uses no additional information on the Hamiltonian away from
the band of interest. Our result is applicable to other time-dependent
semi-classical problems. We discuss semi-classical distributions for the
effective one-particle dynamics and show how they can be translated to the full
dynamics by our results.
