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Second order perturbation theory for embedded eigenvalues

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.

preprint2010arXivOpen access
J. FaupinJ. S. MøllerE. Skibsted
math-phmath.MPmath.SP
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J. FaupinJ. S. MøllerE. Skibsted

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