Spectral theory near thresholds for weak interactions with massive particles

  • Jean-Marie Barbaroux

    Université de Toulon, La Garde, France
  • Jérémy Faupin

    Université de Lorraine, Metz, France
  • Jean-Claude Guillot

    Ecole Polytechnique, Palaiseau, France

Abstract

We consider a Hamiltonian describing the weak decay of the massive vector boson Z0Z^0 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