Physical fields and Clifford algebras II. Neutrino field

TL;DR

This paper models neutrino and antineutrino fields using complex Clifford algebras, providing a natural explanation for the absence of right-handed neutrinos and left-handed antineutrinos.

Contribution

It introduces a Clifford algebra framework to describe neutrino fields, clarifying their handedness properties and the absence of certain neutrino states.

Findings

Neutrino and antineutrino fields are represented by specific subalgebras of a complex Clifford algebra.

The framework explains the absence of right-handed neutrinos and left-handed antineutrinos.

Provides a mathematical basis for neutrino field properties using Clifford algebra structures.

Abstract

The neutrino field is considered in the framework of a complex Clifford algebra $\C_3\cong\C_2\oplus\stackrel{\ast}{\C}_2$. The factor-algebras ${}^{\epsilon}\C_2$ and ${}^{\epsilon}\stackrel{\ast}{\C}_2$, which are obtained by means of homomorphic mappings $\C_3\to\C_2$ and $\C_3\to\stackrel{\ast}{\C}_2$, are identified with the neutrino and antineutrino fields, respectively. In this framework we have natural explanation for absence of right-handed neutrino and left-handed antineutrino.