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Spectral Theory of Massless Pauli-Fierz Models

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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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Authors and Affiliations

  1. CNRS and Département de Mathématiques, Université de Cergy-Pontoise, 95302, Cergy-Pontoise Cedex, France

    V. Georgescu

  2. Département de Mathématiques, Université de Paris Sud, 91405, Orsay Cedex, France

    C. Gérard

  3. FB Mathematik (17), Johannes Gutenberg Universität, 55099, Mainz, Germany

    J.S. Møller

Authors
  1. V. Georgescu
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  2. C. Gérard
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  3. J.S. Møller
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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

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