The dressed nonrelativistic electron in a magnetic field

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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