  We consider a mathematical model of the Fermi theory of weak interactions as
patterned according to the well-known current-current coupling of quantum
electrodynamics. We focuss on the example of the decay of the muons into
electrons, positrons and neutrinos but other examples are considered in the
same way. We prove that the Hamiltonian describing this model has a ground
state in the fermionic Fock space for a sufficiently small coupling constant.
Furthermore we determine the absolutely continuous spectrum of the Hamiltonian
and by commutator estimates we prove that the spectrum is absolutely continuous
away from a small neighborhood of the thresholds of the free Hamiltonian. For
all these results we do not use any infrared cutoff or infrared regularization
even if fermions with zero mass are involved.
