Spectral theory of a mathematical model in Quantum Field Theory for any spin

TL;DR

This paper develops a spectral analysis of a quantum field theory model describing weak decay processes, establishing the Hamiltonian's spectral properties and its mathematical structure.

Contribution

It introduces a generalized mathematical model for weak decay in quantum field theory using Weinberg's formalism, with a self-adjoint Hamiltonian and spectral analysis.

Findings

Hamiltonian is self-adjoint with a unique ground state

Spectrum is absolutely continuous above ground state energy

Model generalizes weak decay of cobalt nucleus

Abstract

In this paper we use the formalism of S.Weinberg in order to construct a mathematical model based on the weak decay of hadrons and nuclei. In particular we consider a model which generalizes the weak decay of the nucleus of the cobalt. We associate with this model a Hamiltonian with cutoffs in a Fock space. The Hamiltonian is self-adjoint and has an unique ground state. By using the commutator theory we get a limiting absorption principle from which we deduce that the spectrum of the Hamiltonian is absolutely continuous above the energy of the ground state and below the first threshold.