Second order perturbation theory for embedded eigenvalues

Abstract

We study second order perturbation theory for embedded eigenvalues of an abstract class of self-adjoint operators. Using an extension of the Mourre theory, under assumptions on the regularity of bound states with respect to a conjugate operator, we prove upper semicontinuity of the point spectrum and establish the Fermi Golden Rule criterion. Our results apply to massless Pauli-Fierz Hamiltonians for arbitrary coupling.

30 pages, 2 figures

References in corpus (3)

• Asymptotic Completeness in Quantum Field Theory: Translation Invariant Nelson Type Models Restricted to the Vacuum and One-Particle Sectors
• A general resonance theory based on Mourre's inequality
• Regularity of Bound States

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