L'électron habillé non relativiste dans un champ magnétique

We consider a nonrelativistic electron interacting with a classical magnetic field pointing along the x3-axis and with a quantized electromagnetic field. Because of the translation invariance along the x3-axis, we consider the reduced Hamiltonian associated with the total momentum along the x3-axis and, after introducing an ultraviolet cutoff and an infrared regularization, we prove that the reduced Hamiltonian has a ground state if the coupling constant and the total momentum along the x3-axis are sufficiently small. Finally, we determine the absolutely continuous spectrum of the reduced Hamiltonian and we prove that the renormalized mass of the electron is greater than its bare one. To cite this article: L. Amour et al., C. R. Acad. Sci. Paris, Ser. I 340 (2005).