Faupin, Jeremy2; Møller, Jacob Schach4; Skibsted, Erik4
1 Department of Mathematical Sciences, Faculty of Science, Aarhus University, Aarhus University2 Universite de Bordeaux 13 Department of Mathematics, Science and Technology, Aarhus University4 Department of Mathematics, Science and Technology, Aarhus University
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.
Communications in Mathematical Physics, 2011, Vol 306, Issue 1, p. 193-228