A note on the Poisson bracket of 2d smeared fluxes in loop quantum gravity

2016, November 25
A. S. Cattaneo and A. Perez
arXiv Preprint
We show that the non-Abelian nature of geometric fluxes - the corner-stone in the 
definition of quantum geometry in the framework of loop quantum gravity (LQG) -
follows directly form the continuum canonical commutations relations of gravity in
connection variables and the validity of the Gauss law. The present treatment 
simplifies previous formulations and thus identifies more clearly the root of the 
discreteness of geometric operators in LQG. Our statement generalizes to arbitrary
gauge theories and relies only on the validity of the Gauss law.