Ordinary Matter in Nonlinear Affine Gauge Theories of Gravitation

TL;DR

This paper develops a framework for incorporating ordinary fermionic matter into nonlinear affine gauge theories of gravity, emphasizing the role of the affine group and Lorentz subgroup in the gauge realization.

Contribution

It introduces a novel nonlinear gauge approach to include fermionic matter in metric-affine gravity theories, expanding the theoretical foundation.

Findings

Framework successfully integrates fermionic matter into affine gauge gravity

Highlights the role of the Lorentz subgroup in matter classification

Provides a basis for further exploration of matter-gravity interactions

Abstract

We present a general framework to include ordinary fermionic matter in the metric--affine gauge theories of gravity. It is based on a nonlinear gauge realization of the affine group, with the Lorentz group as the classification subgroup of the matter and gravitational fields.