Positive commutators and the spectrum of Pauli-Fierz Hamiltonian of atoms and molecules

Volker Bach, Jürg Fröhlich, Israel Michael Sigal, Avy Soffer

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52 Scopus citations


In this paper we study the energy spectrum of the Pauli-Fierz Hamiltonian generating the dynamics of nonrelativistic electrons bound to static nuclei and interacting with the quantized radiation field. We show that, for sufficiently small values of the elementary electric charge, and under weaker conditions than those required in [3], the spectrum of this Hamiltonian is absolutely continuous, except possibly in small neighbourhoods of the ground state energy and the ionization thresholds. In particular, it is shown that (for a large range of energies) there are no stable excited eigenstates. The method used to prove these results relies on the positivity of the commutator between the Hamiltonian and a suitably modified dilatation generator on photon Fock space.

Original languageEnglish (US)
Pages (from-to)557-587
Number of pages31
JournalCommunications In Mathematical Physics
Issue number3
StatePublished - 1999

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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