Affine gauge theory of gravity and its reduction to the Riemann-Cartan geometry

TL;DR

This paper explores a quantum gravity framework based on affine gauge theory, reducing to Riemann-Cartan geometry, and examines the implications of gauge group choices and matter fields for the geometric structure.

Contribution

It introduces a gauge-theoretic approach to quantum gravity using the affine group and analyzes the reduction to Riemann-Cartan geometry, including matter fields from nonmetric degrees of freedom.

Findings

Reduction from affine to orthogonal gauge group introduces matter fields.

The framework harmonizes principles of QFT and general relativity.

Results are independent of initial theoretical assumptions.

Abstract

We discuss a possible framework for the construction of a quantum gravity theory where the principles of QFT and general relativity can coexist harmonically. Moreover, in order to fix the correct gauge group of the theory we study the most general one, the affine group and its natural reduction to the orthogonal group. The price we pay for simplifying the geometry is the presence of matter fields associated with the nonmetric degrees of freedom of the original setup. The result is independent of the starting theory.