Spectral and scattering theory for some abstract QFT Hamiltonians

Details Spectral and scattering theory for some abstract QFT Hamiltonians Spectral and scattering theory for some abstract QFT Hamiltonians

2008-06-27

arxiv.org/abs/0806.4597v1

Rev.Math.Phys.21:373-437,2009

Physics

Mathematical Physics

Scientific paper

10.1142/S0129055X09003645

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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