New constraints for canonical general relativity Original Research Article

Ashtekarʹs canonical theory of classical complex Euclidean GR (no Lorentzian reality conditions) is found to be invariant under the full algebra of infinitesimal 4-diffeomorphisms, but non-invariant under some finite proper 4-diffeos when the densitized dreibein, E∼ia, is degenerate. The breakdown of 4-diffeo invariance appears to be due to the inability of the Ashtekar Hamiltonian to generate births and deaths of E∼ flux loops (leaving open the possibility that a new ‘causality condition’ forbidding the birth of flux loops might justify the non-invariance of the theory).