Nous considérons un électron non relativiste interagissant avec un champ magnétique classique pointant dans la direction et un champ electromagnétique quantifié. L'invariance par translation dans la direction nous amène à considérer l'hamiltonien réduit associé au moment total suivant cette direction. Après l'introduction d'une troncature ultraviolette et d'une régularisation infrarouge appropriées, nous démontrons l'existence d'un état fondamental pour l'opérateur réduit dès que la constante de couplage et le moment total suivant sont suffisament petits. De plus nous déterminons le spectre absolument continu de l'opérateur réduit et nous montrons que la masse renormalisée de l'électron est plus grande que sa masse nue.
We consider a nonrelativistic electron interacting with a classical magnetic field pointing along the -axis and with a quantized electromagnetic field. Because of the translation invariance along the -axis, we consider the reduced Hamiltonian associated with the total momentum along the -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 -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.
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Laurent Amour 1 ; Benoît Grébert 2 ; Jean-Claude Guillot 3, 4
@article{CRMATH_2005__340_6_421_0, author = {Laurent Amour and Beno{\^\i}t Gr\'ebert and Jean-Claude Guillot}, title = {L'\'electron habill\'e non relativiste dans un champ magn\'etique}, journal = {Comptes Rendus. Math\'ematique}, pages = {421--426}, publisher = {Elsevier}, volume = {340}, number = {6}, year = {2005}, doi = {10.1016/j.crma.2005.02.004}, language = {fr}, }
TY - JOUR AU - Laurent Amour AU - Benoît Grébert AU - Jean-Claude Guillot TI - L'électron habillé non relativiste dans un champ magnétique JO - Comptes Rendus. Mathématique PY - 2005 SP - 421 EP - 426 VL - 340 IS - 6 PB - Elsevier DO - 10.1016/j.crma.2005.02.004 LA - fr ID - CRMATH_2005__340_6_421_0 ER -
Laurent Amour; Benoît Grébert; Jean-Claude Guillot. L'électron habillé non relativiste dans un champ magnétique. Comptes Rendus. Mathématique, Volume 340 (2005) no. 6, pp. 421-426. doi : 10.1016/j.crma.2005.02.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.02.004/
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