Spectral Theory for the Weak Decay of Muons in a Uniform Magnetic Field

doi:10.4236/oalib.1105352

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Open Access Library Journal 6 2019

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Spectral Theory for the Weak Decay of Muons in a Uniform Magnetic Field

DOI: 10.4236/oalib.1105352, PP. 1-32

Jean-Claude Guillot

Subject Areas: Particle Physics, Mathematical Analysis

Keywords: Weak Decay of Muons, Fermi’s Theory, Uniform Magnetic Field, Spectral Theory

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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.

Cite this paper

Guillot, J. (2019). Spectral Theory for the Weak Decay of Muons in a Uniform Magnetic Field. Open Access Library Journal, 6, e5352. doi: http://dx.doi.org/10.4236/oalib.1105352.

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