Boost invariance of the gravitational field dynamics: quantization without time gauge

TL;DR

This paper presents a canonical quantization approach for gravity using a 4-bein formulation that preserves boost invariance, avoiding gauge fixing or Lorentz frame fixing, thus maintaining symmetry at the quantum level.

Contribution

It introduces a method for quantizing gravity without fixing the Lorentz frame, ensuring boost invariance remains intact during quantization.

Findings

Boost invariance is preserved in the quantum gravitational dynamics.

Quantization without gauge fixing does not affect Lorentz boost symmetry.

The approach applies to a second-order formulation with a 4-bein.

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.