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Scattering theory for mathematical models of the weak interaction

Benjamin Louis Alvarez

Institut Elie Cartan de Lorraine, Université de Lorraine, 57045 Metz Cedex 1, France

E-mail Address: benjamin.alvarez@univ-lorraine.fr

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and

Jérémy Faupin

Institut Elie Cartan de Lorraine, Université de Lorraine, 57045 Metz Cedex 1, France

E-mail Address: jeremy.faupin@univ-lorraine.fr

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https://doi.org/10.1142/S0129055X20500026Cited by:1 (Source: Crossref)

Abstract

We consider mathematical models of the weak decay of the vector bosons $W^{\pm}$ $W^{\pm}$ into leptons. The free quantum field Hamiltonian is perturbed by an interaction term from the standard model of particle physics. After the introduction of high energy and spatial cut-offs, the total quantum Hamiltonian defines a self-adjoint operator on a tensor product of Fock spaces. We study the scattering theory for such models. First, the masses of the neutrinos are supposed to be positive: for all values of the coupling constant, we prove asymptotic completeness of the wave operators. In a second model, neutrinos are treated as massless particles and we consider a simpler interaction Hamiltonian: for small enough values of the coupling constant, we prove again asymptotic completeness, using singular Mourre’s theory, suitable propagation estimates and the conservation of the difference of some number operators.

Keywords:

AMSC: 81T10, 81U99, 47A40

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