 06340 laurent AMOUR, Benoit GREBERT, JeanClaude GUILLOT
 A mathematical model for the Fermi weak interaction
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Nov 22, 06

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Abstract. We consider a mathematical model of the Fermi theory of
weak interactions as patterned according to the wellknown
currentcurrent 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.
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