Quantized gauge-affine gravity in the superfiber bundle approach

TL;DR

This paper develops a geometric framework for quantizing gauge-affine gravity using superfiber bundles, deriving BRST symmetries and gauge-fixing actions for both gauge-affine and Einstein gravity.

Contribution

It introduces a superfiber bundle formalism for gauge-affine gravity quantization, deriving BRST transformations and gauge-fixing procedures within this geometric approach.

Findings

Derived BRST and anti-BRST transformations for gauge-affine gravity.

Reduced transformations to Einstein's gravity by symmetry breaking.

Provided a method to construct BRST-invariant gauge-fixing actions.

Abstract

The quantization of gauge-affine gravity within the superfiber bundle formalism is proposed. By introducing an even pseudotensorial 1-superform over a principal superfibre bundle with superconnection, we obtain the geometrical Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST transformations of the fields occurring in such a theory. Reducing the four-dimensional general affine group double-covering to the Poincare group double-covering we also find the BRST and anti-BRST transformations of the fields present in Einstein's gravity. Furthermore, we give a prescription leading to the construction of both BRST-invariant gauge-fixing action for gauge-affine gravity and Einstein's gravity.