On the Infrared Problem for the Dressed Non-Relativistic Electron in a Magnetic Field
| dc.creator | Amour, Laurent | |
| dc.creator | Faupin, Jérémy | |
| dc.creator | Grebert, Benoit | |
| dc.creator | Guillot, Jean-Claude | |
| dc.date | 2008-12-18 | |
| dc.date.accessioned | 2026-07-07T12:20:20Z | |
| dc.date.available | 2026-07-07T12:20:20Z | |
| dc.description | We consider a non-relativistic electron interacting with a classical magnetic field pointing along the $x_3$-axis and with a quantized electromagnetic field. The system is translation invariant in the $x_3$-direction and we consider the reduced Hamiltonian $H(P_3)$ associated with the total momentum $P_3$ along the $x_3$-axis. For a fixed momentum $P_3$ sufficiently small, we prove that $H(P_3)$ has a ground state in the Fock representation if and only if $E'(P_3)=0$, where $P_3 \mapsto E'(P_3)$ is the derivative of the map $P_3 \mapsto E(P_3) = \inf σ(H(P_3))$. If $E'(P_3) \neq 0$, we obtain the existence of a ground state in a non-Fock representation. This result holds for sufficiently small values of the coupling constant. | |
| dc.identifier | https://arxiv.org/abs/0812.3562 | |
| dc.identifier | http://arxiv.org/abs/0812.3562 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/213038 | |
| dc.subject | Mathematical Physics | |
| dc.subject | 81V10; 81Q10; 81Q15 | |
| dc.title | On the Infrared Problem for the Dressed Non-Relativistic Electron in a Magnetic Field | |
| dc.type | text |