Weak interactions in a background of a uniform magnetic field. A mathematical model for the inverse beta decay.I

TL;DR

This paper develops a mathematical model for inverse beta decay in a uniform magnetic field, analyzing the Hamiltonian's spectral properties and conditions for a unique ground state without infrared regularization.

Contribution

It introduces a selfadjoint Hamiltonian model for inverse beta decay in magnetic fields, studying its spectrum and ground state properties under small coupling.

Findings

Hamiltonian is selfadjoint with a ground state

Spectrum analysis of the Hamiltonian is provided

Conditions for ground state uniqueness are established

Abstract

In this paper we consider a mathematical model for the inverse beta decay in a uniform magnetic field. With this model we associate a Hamiltonian with cutoffs in an appropriate Fock space. No infrared regularization is assumed. The Hamiltonian is selfadjoint and has a ground state. We study its essential spectrum and determine its spectrum. Conditions for uniqueness of ground state are given. The coupling constant is supposed suffciently small.