 04417 L. Amour, B. Grebert, JC Guillot
 The dressed nonrelativistic electron in a magnetic field
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Dec 17, 04

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Abstract. We consider a nonrelativistic electron interacting
with a classical magnetic field pointing along the $x_{3}$axis and
with a quantized electromagnetic field. When the interaction
between the electron and photons is turned off, the electronic
system is assumed to have a ground state of finite multiplicity.
Because of the translation
invariance along the $x_{3}$axis, we consider the reduced Hamiltonian
associated with the total momentum along the $x_{3}$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 $x_{3}$axis are
sufficiently small. Finally we determine the absolutely continuous
spectrum of the reduced Hamiltonian.
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