The Role of Time Gauge in Quantizing Gravity

TL;DR

This paper develops a Hamiltonian formulation of General Relativity using the Holst action, enabling Loop Quantum Gravity quantization without fixing the Lorentz gauge, thus broadening the framework's applicability.

Contribution

It introduces a generalized Hamiltonian formulation that incorporates the Lorentz gauge freedom, extending Loop Quantum Gravity methods to more general frames.

Findings

Gauss constraint derived in a general Lorentz frame

Loop Quantum Gravity quantization extended without gauge fixing

Framework applicable to broader class of Lorentz frames

Abstract

We present the Hamiltonian formulation of General Relativity with the Holst formulation in a generic local Lorentz frame. In particular, we outline that a Gauss constraint is inferred by a proper generalization of Ashtekar-Barbero-Immirzi connections. This feature allow to extend the Loop Quantum Gravity quantization procedure to the case in which no gauge fixing at all is performed of the Lorentz frame.