Spectral Theory for the Standard Model of Non-Relativistic QED

Details Spectral Theory for the Standard Model of Non-Relativistic QED Spectral Theory for the Standard Model of Non-Relativistic QED

2006-11-07

arxiv.org/abs/math-ph/0611013v2

Physics

Mathematical Physics

37 pages, to appear in CMP

Scientific paper

For a model of atoms and molecules made from static nuclei and non-relativistic electrons coupled to the quantized radiation field (the standard model of non-relativistic QED), we prove a Mourre estimate and a limiting absorption principle in a neighborhood of the ground state energy. As corollaries we derive local decay estimates for the photon dynamics, and we prove absence of (excited) eigenvalues and absolute continuity of the energy spectrum near the ground state energy, a region of the spectrum not understood in previous investigations. The conjugate operator in our Mourre estimate is the second quantized generator of dilatations on Fock space.

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