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Spectral Theory of Pauli–Fierz Operators

✍ Scribed by Jan Dereziński; Vojkan Jakšić

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
423 KB
Volume
180
Category
Article
ISSN
0022-1236

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✦ Synopsis

We study spectral properties of Pauli Fierz operators which are commonly used to describe the interaction of a small quantum system with a bosonic free field. We give precise estimates of the location and multiplicity of the singular spectrum of such operators. 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 Mourre theory applied to the operator restricted to the sector orthogonal to the vacuum. 2001 Academic Press Contents. 1. Introduction. 1.1. The Conjugate Operator Method. 1.2. The Feshbach Method. 1.3. Combining the Feshbach Method with the Mourre Theory. 1.4. Main Results. 1.5. Pauli Fierz Operators. 1.6. From Nonrelativistic QED to Pauli Fierz Hamiltonians. 1.7. Pauli Fierz Liouvilleans. 1.8. Return to Equilibrium. 1.9. Gluing Non-Physical Free Bosons. 1.10. Comparison with the Literature. 1.11. Organization of the Paper. 2. Preliminaries 3.

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