Petras Theory of a Spin-1/2 Particle in Electromagnetic and Gravitational Fields

TL;DR

This paper develops a covariant 20-component wave equation for a spin-1/2 particle with anomalous magnetic moment in electromagnetic and gravitational fields, demonstrating gauge invariance, symmetry properties, and conformal invariance in the massless case.

Contribution

It introduces a generally covariant 20-component wave equation incorporating electromagnetic and gravitational interactions, extending Dirac theory with new conformally invariant equations.

Findings

The equations are consistent with general relativity and gauge symmetry.

A conserved current for the 20-component field is constructed.

New conformally invariant equations are proposed for the massless case.

Abstract

20-component Petras theory of 1/2-spin particle with anomalous magnetic momentum in presence of external electromagnetic and gravitational fields is investigated. The gravitation field is described as space-time curvature. Correctness of the constructed equations in the sense of general relativity and gauge local Lorentz symmetry is proved in detail. Tetrad P-symmetry of the equations is demonstrated. A generally covariant representation of the invariant bilinear form matrix is established and the conserved current of the 20-componen t field is constructed. It is shown that after exclusion of the additional vector-bispinor \Psi_\beta(x) the wave equation for the principal \Psi -bispinor looks as generally covariant Dirac's equation with electromagnetic minimal and Pauli interactions and with an additional gravitational interaction through scalar curvarture R(x)-term. The massless case is analyzed in detail. The conformal non-invariance of the massless equation is demonstrated and new conformally invariant equations for 20-component field are proposed.