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

A self-contained treatment of the linearization procedure for constrai ned Hamiltonian systems is first presented in a general setting. The p rocedure is then applied to general relativity using triads and self-d ual connections as the basic canonical variables. These results have p aved the way to the quantization of weak gravitational waves in the co nnection and loop representations and to a study of the relation betwe en these quanta and nonperturbative canonical gravity. In the classica l theory, they suggest a new approach to the treatment of gravitationa l perturbations and may be useful also to the theory underlying weak g ravity waves.