Stefan Teufel, Herbert Spohn Semi-classical motion of dressed electrons (92K, Latex2e) ABSTRACT. 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 $H_{\rm PF}$ enter. Most importantly, $H_{\rm PF}$ must have an isolated ground state band for $|p|< p_{\rm c}\leq \infty$ with $p$ the total momentum and $p_{\rm c}$ 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|