JEAN-CLAUDE GUILLOT WEAK INTERACTIONS IN A BACKGROUND OF A UNIFORM MAGNETIC FIELD. A MATHEMATICAL MODEL FOR THE INVERSE β DECAY.I. (104K, LateX) ABSTRACT. In this paper we consider a mathematical model for the in- verse β 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 self-adjoint and has a unique ground state. We study the essential spectrum and determine the spectrum. The coupling constant is supposed sufficiently small.