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

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Document pages: 31 pages

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.

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