Comptes Rendus
Mathematical Physics
Limiting absorption principle at low energies for a mathematical model of weak interaction: The decay of a boson
[Propriétés spectrales et principe d'absorption limite à faible énergie pour un modèle mathématique d'interaction faible : La désintégration d'un boson]
Comptes Rendus. Mathématique, Volume 347 (2009) no. 17-18, pp. 1087-1092.

Nous étudions les propriétés spectrales d'un hamiltonien qui décrit la désintégration du boson massif W±, de spin 1. Nous démontrons que ce hamiltonien est auto-adjoint, que l'infimum de son spectre est une valeur propre simple. Nous montrons par ailleurs une inégalité de Mourre et un principe d'absorption limite pour les énergies en dessous du premier seuil. Comme corollaire, nous obtenons le caractère purement absolument continu du spectre pour ces mêmes énergies.

We study the spectral properties of a Hamiltonian describing the weak decay of spin 1 massive bosons into the full family of leptons. We prove that the considered Hamiltonian is self-adjoint, with a unique ground state and we derive 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 absence of eigenvalues and absolute continuity of the energy spectrum in the same spectral interval.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.07.014
Jean-Marie Barbaroux 1, 2 ; Jean-Claude Guillot 3

1 Centre de physique théorique, Luminy case 907, 13288 Marseille cedex 9, France
2 Département de mathématiques, université du Sud Toulon-Var, 83957 La Garde cedex, France
3 Centre de mathématiques appliquées, UMR 7641, École polytechnique – CNRS, 91128 Palaiseau cedex, France
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     author = {Jean-Marie Barbaroux and Jean-Claude Guillot},
     title = {Limiting absorption principle at low energies for a mathematical model of weak interaction: {The} decay of a boson},
     journal = {Comptes Rendus. Math\'ematique},
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Jean-Marie Barbaroux; Jean-Claude Guillot. Limiting absorption principle at low energies for a mathematical model of weak interaction: The decay of a boson. Comptes Rendus. Mathématique, Volume 347 (2009) no. 17-18, pp. 1087-1092. doi : 10.1016/j.crma.2009.07.014. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.07.014/

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[3] J.-M. Barbaroux; J.-C. Guillot Spectral theory for a mathematical model of the weak interaction: The decay of the intermediate vector bosons W±, I. (preprint) | arXiv

[4] J. Fröhlich; M. Griesemer; I.M. Sigal Spectral theory for the standard model of non-relativistic QED, Comm. Math. Phys., Volume 283 (2008) no. 3, pp. 613-646

[5] J. Glimm; A. Jaffe Quantum Field Theory and Statistical Mechanics, Birkhäuser, Boston Inc., Boston, MA, 1985 (Expositions, Reprint of articles published in 1969–1977)

[6] W. Greiner; B. Müller Gauge Theory of Weak Interactions, Springer, Berlin, 1989

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[10] S. Weinberg The Quantum Theory of Fields, vol. II, Modern Applications, Cambridge University Press, Cambridge, 2005

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