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Second order perturbation theory for embedded eigenvalues

Mathematical Physics 2011-07-21 v1 math.MP Spectral Theory

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.

Keywords

Cite

@article{arxiv.1006.5869,
  title  = {Second order perturbation theory for embedded eigenvalues},
  author = {J. Faupin and J. S. Møller and E. Skibsted},
  journal= {arXiv preprint arXiv:1006.5869},
  year   = {2011}
}

Comments

30 pages, 2 figures

R2 v1 2026-06-21T15:42:57.236Z