Spectral and scattering theory for some abstract QFT Hamiltonians
| dc.creator | Gérard, Christian | |
| dc.creator | Panati, Annalisa | |
| dc.date | 2008-06-27 | |
| dc.date.accessioned | 2026-07-07T13:06:09Z | |
| dc.date.available | 2026-07-07T13:06:09Z | |
| dc.description | We introduce an abstract class of bosonic QFT Hamiltonians and study their spectral and scattering theories. These Hamiltonians are of the form $H=\d\G(ω)+ V$ acting on the bosonic Fock space $\G(\ch)$, where $ω$ is a massive one-particle Hamiltonian acting on $\ch$ and $V$ is a Wick polynomial $\Wick(w)$ for a kernel $w$ satisfying some decay properties at infinity. We describe the essential spectrum of $H$, prove a Mourre estimate outside a set of thresholds and prove the existence of asymptotic fields. Our main result is the {\em asymptotic completeness} of the scattering theory, which means that the CCR representations given by the asymptotic fields are of Fock type, with the asymptotic vacua equal to the bound states of $H$. As a consequence $H$ is unitarily equivalent to a collection of second quantized Hamiltonians. | |
| dc.identifier | https://arxiv.org/abs/0806.4597 | |
| dc.identifier | http://arxiv.org/abs/0806.4597 | |
| dc.identifier | Rev.Math.Phys.21:373-437,2009 | |
| dc.identifier | doi:10.1142/S0129055X09003645 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/227688 | |
| dc.subject | Mathematical Physics | |
| dc.title | Spectral and scattering theory for some abstract QFT Hamiltonians | |
| dc.type | text |