Abstract :
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).
