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Article Dans Une Revue Reviews in Mathematical Physics Année : 2009

Spectral and scattering theory for some abstract QFT Hamiltonians

Résumé

We introduce an abstract class of bosonic QFT Hamiltonians and study their spectral and scattering theories. These Hamiltonians are of the form $H=\d\G(\omega)+ V$ acting on the bosonic Fock space $\G(\ch)$, where $\omega$ 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.
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Dates et versions

hal-00290672 , version 1 (26-06-2008)

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Christian Gérard, Annalisa Panati. Spectral and scattering theory for some abstract QFT Hamiltonians. Reviews in Mathematical Physics, 2009, 21 (3), pp.373. ⟨10.1142/S0129055X09003645⟩. ⟨hal-00290672⟩
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