On the Hamiltonian of general relativity (Q1080674)

The aim of this report is to review some of the recent developments in the Hamiltonian description of general relativity. The essential point behind these developments is the realization that one can introduce, on the phasespace of asymptotically flat gravitational fields, certain variables (or, coordinates) in terms of which the Hamiltonians generating translations assume an especially simple form. The simplification brought about is both conceptual and technical. An important consequence is that one can now see that the Hamiltonians generating (future-directed) time- translations are manifestly nonnegative and vanish only at those points of the phase space which correspond to Cauchy data for Minkowski space. These developments have opened up certain avenues for the canonical quantization of the theory which have already provided some encouraging results. However, since this report belongs to the session on classical field theory and general relativity, here I will confine my discussion to the classical theory.