The Continuum Limit of a Fermion System Involving Neutrinos: Weak and Gravitational Interactions

We analyze the causal action principle for a system of relativistic fermions composed of massive Dirac particles and neutrinos. In the continuum limit, we obtain an effective interaction described by a left-handed, massive SU(2) gauge field and a gravitational field. The off-diagonal gauge potentials involve a unitary mixing matrix, which is similar to the Maki-Nakagawa-Sakata matrix in the standard model.