Second order perturbation theory for embedded eigenvalues

Details Second order perturbation theory for embedded eigenvalues Second order perturbation theory for embedded eigenvalues

2010-06-30

arxiv.org/abs/1006.5869v1

Commun.Math.Phys.306:193-228,2011

Physics

Mathematical Physics

30 pages, 2 figures

Scientific paper

10.1007/s00220-011-1278-x

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.

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