Gravitomagnetic Moments of the Fundamental Fields

TL;DR

This paper investigates the gravitational gyromagnetic ratios of fundamental fields, revealing specific ratios for Dirac spinors and vector fields in curved spacetime, and discusses their implications for deriving Dirac equations from vector field equations.

Contribution

It identifies the gravitational gyromagnetic ratios for Dirac and vector fields and shows how these ratios are essential for deriving the Dirac equation from a vector field equation in curved spacetime.

Findings

Dirac spinor interacts with curvature with ppa_S=2

Vector field interacts with curvature with ppa_S=1

Dirac equation can be derived as the square-root of the vector field equation when ratios are correctly included

Abstract

The quadratic form of the Dirac equation in a Riemann spacetime yields a gravitational gyromagnetic ratio \kappa_S = 2 for the interaction of a Dirac spinor with curvature. A gravitational gyromagnetic ratio \kappa_S = 1 is also found for the interaction of a vector field with curvature. It is shown that the Dirac equation in a curved background can be obtained as the square--root of the corresponding vector field equation only if the gravitational gyromagnetic ratios are properly taken into account.