2004/12/20 by Amour, L., Grebert, B., Guillot, J. -C.
#81V05 #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.math-ph/0412069
We consider a nonrelativistic electron interacting with a classical magnetic field pointing along the x3-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 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.