Gauging gravity with SO(1,3) for spin-1/2 particles

TL;DR

This paper explores the geometric and gauge-theoretic foundations of gravity using the Lorentz group SO(1,3), deriving field equations and analyzing the Dirac equation for spin-1/2 particles in gravitational fields.

Contribution

It constructs gravity and spin-1/2 particle equations based on gauge principles and examines their weak field and Schrödinger limits in specific geometries.

Findings

Derived gravity field equations from gauge considerations.

Analyzed Dirac equation limits in Fermi normal and Kerr geometries.

Identified electromagnetic analogs in gravitational interaction terms.

Abstract

We demonstrate, by analogy with electromagnetism, that the geometric content in the theory of gravity is an indirect consequence of the fact that the gauge group in question is the Lorentz group SO(1,3). We hence construct field equations for gravity and a spin-1/2 particle in a gravitational field based on gauge considerations. Furthermore, we derive the weak field and Schroedinger limits of the Dirac equation of the particle in the gravitational field, especially in Fermi normal coordinates and on the equatorial plane of the Kerr geometry, following which we identify the terms to which the electromagnetic potentials A and Phi are analogous.