Second order perturbation theory for embedded eigenvalues
by J. Faupin, J.S. Møller and E. Skibsted
Preprints
Number 5 (July 2010)
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.