Avoiding degenerate coframes in an affine gauge approach to quantum gravity

TL;DR

This paper demonstrates how restoring the inhomogeneous gauge transformation component in an affine gauge approach to quantum gravity prevents degenerate coframes, facilitating more robust path integral quantization.

Contribution

It introduces a method to avoid degenerate coframes in quantum gravity models by explicitly restoring the inhomogeneous part of gauge transformations in the affine gauge framework.

Findings

Restoring the inhomogeneous gauge component prevents coframe degeneracy.

Avoiding degeneracy improves the path integral quantization process.

The approach clarifies the gauge structure of quantum gravity models.

Abstract

In quantum models of gravity, it is surmized that configurations with degenerate coframes could occur during topology change of the underlying spacetime structure. However, the coframe is not the true Yang--Mills type gauge field of the translations, since it lacks the inhomogeneous gradient term in the gauge transformations. By explicitly restoring this ``hidden" piece within the framework of the affine gauge approach to gravity, one can avoid the metric or coframe degeneracy which would otherwise interfere with the integrations within the path integral. This is an important advantage for quantization.