A nonlinear gauge-invariant field theory of leptons

A nonlinear, singularity-free, gauge-invariant field theory of leptons is proposed which incorporates the electron, muon, and tau. Fitting the known masses leads to a lepton radius of the order 10^–16 cm, which is within the experimental range. The model considered suggests the possibility of a hierarchy of short-lived lepton states. Properties of the electron such as its energy-density distribution, Reissner-Nordström repulsion, and the fact that gravitation cannot play a significant role in its construction are discussed. All singularity-free charged particle models constructed from fields which were investigated approached the limit charge²= mass² (in geometrical units) as gravitation became a dominant force. It is suggested that this property may have great generality. The interaction-energy integrals which bind the particles are seen to increase as the energy increases, and it is suggested that a similar mechanism may also be responsible for quark confinement in hadrons.On leave from the Department of Physics and Astronomy, University of Victoria, Victoria, B.C., Canada V8W 2Y2.