Diffeomorphism covariance of the canonical Barbero-Immirzi-Holst triad theory

TL;DR

This paper derives the phase space generator for four-dimensional diffeomorphisms in the Barbero-Immirzi-Holst theory directly from Noether's second theorem, aiding the construction of classical invariants.

Contribution

It provides the first direct derivation of the diffeomorphism generator in this theory from Noether's theorem, clarifying its covariance properties.

Findings

Derived the phase space generator from Noether's second theorem

Reviewed its role in constructing classical diffeomorphism invariants

Clarified the covariance structure of the theory

Abstract

The vanishing phase space generator of the full four-dimensional diffeomorphism-related symmetry group in the context of the Barbero-Immirzi-Holst Lagrangian is derived directly for the first time from Noether's second theorem. Its applicability in the construction of classical diffeomorphism invariants is reviewed.