Identifying metric spinor phase with axion field from axion-fermion coupling and Weyl-Peccei Quinn spin transformations

TL;DR

This paper extends previous work by demonstrating that the metric spinor phase in the Dirac-fermion system can be identified with the axion field, using spin transformations and analyzing the Dirac-Maxwell system.

Contribution

It introduces a method to identify the metric spinor phase with the axion field within Dirac theory, expanding the previous Maxwell-based approach.

Findings

The metric spinor phase behaves as the axion field under spin transformations.

The Dirac-Maxwell system provides a minimal Lagrangian framework for the axion.

Explicit 2-spinor description of magnetic monopole and charge is obtained.

Abstract

Metric spinor phase of the Infeld-van der Waerden {\gamma}-formalism and axion field were identified in Ref. [1], by using Maxwell theory. Since axion couples with fermions, we will investigate Dirac theory to extend the work given in [1], showing that is possible again to identify this phase with the axion. By searching an exact identification, we will work yet the spin transformations to adapt chiral rotations and so to show that the metric spinor phase behaves exactly as required for the axion field. We will study also the Dirac-Maxwell system which provides a minimal Lagrangian approach for the axion classical sector and, finally, we will obtain an explicit 2-spinor description of magnetic monopole and its charge.