TITLE:
Spectral Theory for the Weak Decay of Muons in a Uniform Magnetic Field
AUTHORS:
Jean-Claude Guillot
KEYWORDS:
Weak Decay of Muons, Fermi’s Theory, Uniform Magnetic Field, Spectral Theory
JOURNAL NAME:
Open Access Library Journal,
Vol.6 No.5,
May
23,
2019
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 Hamiltonian 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.