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.
Nous étudions les propriétés spectrales d'un hamiltonien qui décrit la désintégration du boson massif , 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.
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@article{CRMATH_2009__347_17-18_1087_0,
author = {Barbaroux, Jean-Marie and Guillot, Jean-Claude},
title = {Limiting absorption principle at low energies for a mathematical model of weak interaction: {The} decay of a boson},
journal = {Comptes Rendus. Math\'ematique},
pages = {1087--1092},
publisher = {Elsevier},
volume = {347},
number = {17-18},
year = {2009},
doi = {10.1016/j.crma.2009.07.014},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2009.07.014/}
}
TY - JOUR AU - Barbaroux, Jean-Marie AU - Guillot, Jean-Claude TI - Limiting absorption principle at low energies for a mathematical model of weak interaction: The decay of a boson JO - Comptes Rendus. Mathématique PY - 2009 SP - 1087 EP - 1092 VL - 347 IS - 17-18 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2009.07.014/ DO - 10.1016/j.crma.2009.07.014 LA - en ID - CRMATH_2009__347_17-18_1087_0 ER -
%0 Journal Article %A Barbaroux, Jean-Marie %A Guillot, Jean-Claude %T Limiting absorption principle at low energies for a mathematical model of weak interaction: The decay of a boson %J Comptes Rendus. Mathématique %D 2009 %P 1087-1092 %V 347 %N 17-18 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2009.07.014/ %R 10.1016/j.crma.2009.07.014 %G en %F CRMATH_2009__347_17-18_1087_0
Barbaroux, Jean-Marie; Guillot, Jean-Claude. 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. http://www.numdam.org/articles/10.1016/j.crma.2009.07.014/
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