The role of the time gauge in the 2nd order formalism

TL;DR

This paper investigates the impact of the time gauge choice on the canonical quantization of gravity within a second-order formalism, demonstrating that boost invariance remains unaffected regardless of gauge fixing.

Contribution

It shows that quantizing gravity with a 4-bein configuration variable without fixing the Lorentz frame preserves boost invariance.

Findings

Boost invariance is unaffected by gauge fixing.

Quantization using a 4-bein configuration variable maintains Lorentz symmetry.

The approach applies to non-adapted space-time splittings.

Abstract

We perform a canonical quantization of gravity in a second-order formulation, taking as configuration variables those describing a 4-bein, not adapted to the space-time splitting. We outline how, neither if we fix the Lorentz frame before quantizing, nor if we perform no gauge fixing at all, is invariance under boost transformations affected by the quantization.