Gravitational quantum states as finite representations of the Lorentz group

TL;DR

This paper presents a Lorentz-covariant formulation of Loop Quantum Gravity using finite-dimensional Lorentz group representations, incorporating discrete symmetries and connecting to particle classification, resulting in a parameter-free quantum model.

Contribution

It introduces a Lorentz-covariant LQG framework with finite-dimensional representations, eliminating the Immirzi parameter and linking to Wigner's particle classification.

Findings

Formulation accounts for parity and time-reversal symmetries.

The model is free of the Immirzi parameter.

The scalar constraint reduces to the Euclidean part.

Abstract

A manifestly Lorentz-covariant formulation of Loop Quantum Gravity (LQG) is given in terms of finite-dimensional representations of the Lorentz group. The formulation accounts for discrete symmetries, such as parity and time-reversal, and it establishes a link with Wigner classification of particles. The resulting quantum model can be seen as LQG with the internal $SU(2)\otimes SU(2)$ group and it is free of the Immirzi parameter, while the scalar constraint is just the Euclidean part.