Gauge invariant nonlocal theory of the weak interactions

Abstract

The perturbation theory of electromagnetic and weak interactions is considered. A hypothesis is proposed that the neutrino is a “carrier” of nonlocality. It means effectively a nonlocal change of the neutrino free-particle propagator. The charged lepton fields (electron and muon fields) are considered to be local; consequently, the gauge invariance of the theory is guaranteed. The introduction of the nonlocality does not remove all ultraviolet divergences in perturbation theory, but there is number of divergent Feynman diagrams that are formed by the closed charged lepton loops. Therefore, the theory is renormalized. The renormalization of the theory leads to the appearance of an additional pure ν - ν interaction.