SU(2) gauge symmetry in gravity phase space

TL;DR

This paper analyzes the Hamiltonian formulation of the Holst action in gravity, revealing how SU(2) gauge symmetry emerges through constraint reduction, with implications for Loop Quantum Gravity and Spin Foam models.

Contribution

It demonstrates how the SU(2) gauge symmetry naturally arises in the Hamiltonian framework of the Holst action, clarifying its role in quantum gravity approaches.

Findings

SU(2) gauge symmetry is derived from the set of constraints.

The approach clarifies the connection between the Holst action and quantum gravity models.

Implications for Loop Quantum Gravity and Spin Foam are discussed.

Abstract

The Hamiltonian formulation of the Holst action in vacuum and in the presence of matter fields is analyzed in a generic local Lorentz frame. It is elucidated how the SU(2) gauge symmetry is inferred by reducing the set of constraints to a first-class one. The consequences of the proposed approach for Loop Quantum Gravity and Spin Foam models are discussed.