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

TL;DR

This paper investigates the continuum limit of a relativistic fermion system with neutrinos, deriving an effective theory that includes weak and gravitational interactions, featuring a gauge field and a mixing matrix similar to the standard model.

Contribution

It introduces a novel continuum limit analysis of a fermion-neutrino system, deriving an effective interaction with a gauge field and mixing matrix akin to the standard model.

Findings

Effective interaction described by a left-handed SU(2) gauge field and gravity.

Emergence of a mixing matrix similar to the Maki-Nakagawa-Sakata matrix.

Continuum limit provides insights into fermion-neutrino interactions.

Abstract

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.