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arXiv · 1006.5869

Second order perturbation theory for embedded eigenvalues

J. Faupin·J. S. Møller·E. Skibsted
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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.

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J. Faupin, J. S. Møller, E. Skibsted. 2010-06-30. Second order perturbation theory for embedded eigenvalues. https://doi.org/10.1007/s00220-011-1278-x

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