Metric-Affine Gauge Theory of Gravity I. Fundamental Structure and Field Equations

TL;DR

This paper introduces the metric-affine gauge theory of gravity, establishing its geometric and dynamical foundations, and explores subcases including general relativity as a gauge theory of translations.

Contribution

It provides a self-contained derivation of metric-affine gravity from gauge principles, linking it to classical field theory and clarifying its relation to general relativity.

Findings

Derived the geometry of metric-affine gravity.

Established the dynamical framework for the theory.

Explained the gauge origin of general relativity.

Abstract

We give a self-contained introduction into the metric-affine gauge theory of gravity. Starting from the equivalence of reference frames, the prototype of a gauge theory is presented and illustrated by the example of Yang-Mills theory. Along the same lines we perform a gauging of the affine group and establish the geometry of metric-affine gravity. The results are put into the dynamical framework of a classical field theory. We derive subcases of metric-affine gravity by restricting the affine group to some of its subgroups. The important subcase of general relativity as a gauge theory of translations is explained in detail.