# Spectral theory for the weak decay of muons in a uniform magnetic field

## TL;DR

This paper develops a rigorous mathematical framework for analyzing the weak decay of muons in a magnetic field, establishing spectral properties of the associated Hamiltonian without infrared regularization.

## Contribution

It introduces a self-adjoint Hamiltonian model for muon decay in a magnetic field within Fermi theory, analyzing its spectral characteristics and asymptotic behavior.

## Key findings

- Hamiltonian is self-adjoint with a unique ground state
- Essential spectrum is specified and asymptotic fields are constructed
- Absolutely continuous spectrum is characterized

## Abstract

In this article we consider a mathematical model for the weak decay of muons in a uniform magnetic field according to the Fermi theory of weak interactions with V-A coupling. With this model we associate a Hamil-tonian with cutoffs in an appropriate Fock space. No infrared regularization is assumed. The Hamiltonian is self-adjoint and has a unique ground state. We specify the essential spectrum and prove the existence of asymptotic fields from which we determine the absolutely continuous spectrum. The coupling constant is supposed sufficiently small.