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

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.