A Spin Gauge Formulation of Gravity and a New View of Gravity-Matter Interactions

TL;DR

This paper introduces a novel first-order gauge formulation of gravity using SL(2,C) connections and spinor fields, offering a new perspective on gravity-matter interactions by resembling gauge theories.

Contribution

It develops a first-order gravity formulation with spinor-valued fields, providing a new framework to understand gravity-matter interactions in gauge theory terms.

Findings

Derived an action resembling gauge theories for gravity.

Proposed a unified approach to gravity and matter interactions.

Suggested potential insights into gravity's coupling with other forces.

Abstract

A first-order formulation of gravity is developed in which the fundamental fields consist of an SL(2,C) connection and two spinor-valued 1-forms. It is shown that the first term of an expansion of the Einstein-Hilbert action leads to an action for these fields which consists of dynamic L2 inner products of their covariant derivatives, resembling reasonable generalisations of the terms found in the actions of typical gauge theories on Minkowski spacetime. If additional terms corresponding to other forces and matter, formulated in the same manner, are then included, this approach may shed new light on interactions of gravity with matter and other force carriers.