Spectral Theory for a Mathematical Model of the Weak Interaction—Part I : The Decay of the Intermediate Vector Bosons W±

Abstract EN

We consider a Hamiltonian with cutoffs describing the weak decay of spin 1 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 the absence of eigenvalues and absolute continuity of the energy spectrum in the same spectral interval.