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Spectral Theory of Massless Pauli-Fierz Models

Abstract

We study the spectral theory of massless Pauli-Fierz models using an extension of the Mourre method. We prove the local finiteness of point spectrum and a limiting absorption principle away from the eigenvalues for an arbitrary coupling constant. In addition we show that the expectation value of the number operator is finite on all eigenvectors.

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Correspondence to V. Georgescu.

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Communicated by H. Spohn

Supported by Carlsbergfondet

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Georgescu, V., Gérard, C. & Møller, J. Spectral Theory of Massless Pauli-Fierz Models. Commun. Math. Phys. 249, 29–78 (2004). https://doi.org/10.1007/s00220-004-1111-x

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  • DOI: https://doi.org/10.1007/s00220-004-1111-x

Keywords

  • Spectral Theory
  • Point Spectrum
  • Number Operator
  • Local Finiteness
  • Limit Absorption Principle