Spectral theory for a mathematical model of the weak interaction: The decay of the intermediate vector bosons W+/-. I

TL;DR

This paper analyzes a mathematical model of weak boson decay, proving spectral properties like absence of eigenvalues and spectrum continuity using Mourre theory.

Contribution

It establishes spectral properties of a Hamiltonian modeling W boson decay, including Mourre estimates and absence of eigenvalues, for the first time in this context.

Findings

Proved Mourre estimate for the Hamiltonian

Established absence of eigenvalues in the spectral interval

Showed absolute continuity of the energy spectrum

Abstract

We consider a Hamiltonian with cutoffs describing the weak decay of spin one massive bosons into the full family of leptons. The Hamiltonian is a self-adjoint operator in an appropriate Fock space with a unique ground state. We prove a Mourre estimate and a limiting absorption principle above the ground state energy and below the first threshold for a sufficiently small coupling constant. As a corollary, we prove absence of eigenvalues and absolute continuity of the energy spectrum in the same spectral interval.