Limiting absorption principle at low energies for a mathematical model of weak interaction: The decay of a boson

Abstract

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. To cite this article: J.-M. Barbaroux, J.-C. Guillot, C. R. Acad. Sci. Paris, Ser. I 347 (2009).