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Journal of Spectral Theory

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Volume 9, Issue 2, 2019, pp. 453–512
DOI: 10.4171/JST/253

Published online: 2018-10-24

Local decay for weak interactions with massless particles

Jean-Marie Barbaroux[1], Jérémy Faupin[2] and Jean-Claude Guillot[3]

(1) Université de Toulon, France
(2) Université de Lorraine, Metz, France
(3) École Polytechnique, Palaiseau, France

We consider a mathematical model for the weak decay of the intermediate boson $Z^0$ into neutrinos and antineutrinos. We prove that the total Hamiltonian has a unique ground state in Fock space and we establish a limiting absorption principle, local decay and a property of relaxation to the ground state for initial states and observables suitably localized in energy and position. Our proofs rest, in particular, on Mourre’s theory and a low-energy decomposition.

Keywords: Standard model, weak interactions, spectral theory, Mourre theory, local decay

Barbaroux Jean-Marie, Faupin Jérémy, Guillot Jean-Claude: Local decay for weak interactions with massless particles. J. Spectr. Theory 9 (2019), 453-512. doi: 10.4171/JST/253