Spectral theory near thresholds for weak interactions with massive particles
Jean-Marie Barbaroux
Université de Toulon, La Garde, FranceJérémy Faupin
Université de Lorraine, Metz, FranceJean-Claude Guillot
Ecole Polytechnique, Palaiseau, France
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Abstract
We consider a Hamiltonian describing the weak decay of the massive vector boson into electrons and positrons. We show that the spectrum of the Hamiltonian is composed of a unique isolated ground state and a semi-axis of essential spectrum. Using an infrared regularization and a suitable extension of Mourre’s theory, we prove that the essential spectrum below the boson mass is purely absolutely continuous.
Cite this article
Jean-Marie Barbaroux, Jérémy Faupin, Jean-Claude Guillot, Spectral theory near thresholds for weak interactions with massive particles. J. Spectr. Theory 6 (2016), no. 3, pp. 505–555
DOI 10.4171/JST/131