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Advances in Mathematical Physics
Volume 2009, Article ID 978903, 52 pages
Research Article

Spectral Theory for a Mathematical Model of the Weak Interaction—Part I: The Decay of the Intermediate Vector Bosons 𝑊±

1Centre de Physique Théorique, Centre National de la Recherche Scientique (CNRS), Luminy Case 907, 13288 Marseille Cedex 9, France
2Département de Mathématiques, Université du Sud Toulon-Var, 83957 La Garde Cedex, France
3Centre de Mathématiques Appliquées, École Polytechnique, UMR-CNRS 7641, 91128 Palaiseau Cedex, France

Received 28 April 2009; Accepted 13 August 2009

Academic Editor: Valentin Zagrebnov

Copyright © 2009 J.-M. Barbaroux and J.-C. Guillot. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider a Hamiltonian with cutoffs describing the weak decay of spin 1 massive bosons into the full family of leptons. The Hamiltonian is a self-adjoint operator in an appropriate Fock space with a unique ground state. We prove a Mourre estimate and a limiting absorption principle above the ground state energy and below the first threshold for a sufficiently small coupling constant. As a corollary, we prove the absence of eigenvalues and absolute continuity of the energy spectrum in the same spectral interval.