Gauge Formalism for General Relativity and Fermionic Matter

TL;DR

This paper introduces a gauge-theoretic formalism for describing fermionic matter in curved spacetime, replacing the metric with spin frames, and derives conserved quantities within this framework.

Contribution

It develops a new gauge formalism for spinors in curved spaces, integrating gravity and fermions through a gauge structure and calculating conserved quantities.

Findings

Formalism describes interaction between gravity and spinors.

Replaces metric with spin frames in General Relativity.

Calculates conserved quantities and superpotentials.

Abstract

A new formalism for spinors on curved spaces is developed in the framework of variational calculus on fibre bundles. The theory has the same structure of a gauge theory and describes the interaction between the gravitational field and spinors. An appropriate gauge structure is also given to General Relativity, replacing the metric field with spin frames. Finally, conserved quantities and superpotentials are calculated under a general covariant form.