The Gauge Group in the Ashtekar-Barbero Formulation of Canonical Gravity

It still not universally recognized that all the gauge symmetries present in the Lagrangian formalism for a physical theory must also manifest themselves in the canonical formalism. This issue has been particularly obscure and controversial in the case of generally covariant theories, where the full realization of the diffeomorphisms-induced gauge group in phase space has met with the difficulty of the lack of projectability of some generators from the configuration-velocity space to phase space...