Space Inversion of Spinors Revisited: A Possible Explanation of Chiral Behavior in Weak Interactions

TL;DR

This paper explores a Clifford algebra-based model of spinors to explain the chiral nature of weak interactions, proposing a left-right symmetric system with mirror particles and generalized gauge fields.

Contribution

It introduces a novel Clifford algebra framework where spinors transform between ideals under space inversion, linking this to the origin of chirality in weak interactions.

Findings

Space inversion transforms spinors between different ideals.

The model incorporates SU(2) gauge fields as components of a generalized spin connection.

A left-right symmetric system with mirror particles is proposed.

Abstract

We investigate a model in which spinors are considered as being embedded within the Clifford algebra that operates on them. In Minkowski space $M_{1,3}$, we have four independent 4-component spinors, each living in a different minimal left ideal of $Cl(1,3)$. We show that under space inversion, a spinor of one left ideal transforms into a spinor of another left ideal. This brings novel insight to the role of chirality in weak interactions. We demonstrate the latter role by considering an action for a generalized spinor field $\psi^{\alpha i}$ that has not only a spinor index $\alpha$ but also an extra index $i$ running over four ideals. The covariant derivative of $\psi^{\alpha i}$ contains the generalized spin connection, the extra components of which are interpreted as the SU(2) gauge fields of weak interactions and their generalization. We thus arrive at a system that is left-right symmetric due to the presence of a "parallel sector", postulated a long time ago, that contains mirror particles coupled to mirror SU(2) gauge fields.