MPS-RR 1999-3
January 1999

Spectral theory of Pauli-Fierz Hamiltonians I.

by:

Jan Derezinski, Vojkan Jaksic

Abstract

We study spectral properties of Pauli-Fierz Hamiltonians which are commonly used to describe the interaction of a small quantum system with a bosonic free field. We give precise estimates on the location and multiplicity of the singular spectrum of such Hamiltonians. Applications of these estimates, which will be discussed elsewhere, concern spectral and ergodic theory of non-relativistic QED. Our proof has two ingredients: the Feshbach method, which is developed in an abstract framework, and the Mourre method applied to the Hamiltonian restricted to the sector orthogonal to the vacuum.

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This paper has now been published in J. Funct. Anal. 180 (2001), no. 2, 243--327.