WEAK-FIELD LIMIT OF GENERAL-RELATIVITY IN TERMS OF NEW VARIABLES - A HAMILTONIAN FRAMEWORK

A self-contained treatment of the linearization procedure for constrained Hamiltonian systems is first presented in a general setting. The procedure is then applied to general relativity using triads and self-dual connections as the basic canonical variables. These results have paved the way to the quantization of weak gravitational waves in the connection and loop representations and to a study of the relation between these quanta and nonperturbative canonical gravity. In the classical theory, they suggest a new approach to the treatment of gravitational perturbations and may be useful also to the theory underlying weak gravity waves.