Theory of Leptons

Abstract

A unified theory describing four leptons, i.e., muon, electron and two neutrinos together is presented. Leptons are represented by a single fundamental field: Without any interaction the field satisfies a fourth-order differential wave equation. When the influence of the electromagnetic field is taken into account, the appearance of reactive terms in the equation makes it possible to decompose the fundamental field into two Dirac fields (electrons's and muon's) and a residual field. Though the residual field interacts with the electromagnetic field in a way similar to the separated two Dirac fields, the corresponding phenomena are shown to be ineffective owing to the mechanism analogous to Bleuler and Gupta's in quantum electrodynamics, provided the right (or left) handed component of the residual field is assumed not to exist: The proposed nonlocal weak interaction of the fundamental field leads to the coupling, on the mass shell, of the charge exchange current-current type. The current of approximate V - A with small T-mixture type gives the neutrino a small mass, which causes the separation of one neutrino field from the other. From these investigations, the following problems are suggested: i) The existence of two kinds of neutral lepton fields with nearly zero mass would be understood in connection with their appearance through the two-component parts in nature. ii) There would be a possible description of one pair of lepton (for instance, muon and massive neutrino) by means of the indefinite metric in Hilbert space, which is suggested by the existence of two kinds of lepton number conservation. iii) In connection with the occurrence of lepton weak interaction, at least one of the masses of neutrinos, should be finite (non-zero), but less than the electron mass.