We consider a mathematical model for the weak decay of the intermediate boson 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.
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Jean-Marie Barbaroux, Jérémy Faupin, Jean-Claude Guillot, Local decay for weak interactions with massless particles. J. Spectr. Theory 9 (2019), no. 2, pp. 453–512DOI 10.4171/JST/253