36 v 1 9 O ct 1 99 8 The N - body Problem in Tetrad Gravity : a First Step towards the Unified

After a review of the canonical reduction to the rest-frame Wigner-covariant instant form of standard theories in Minkowski spacetime, a new formulation of tetrad gravity is introduced. Its canonical reduction, also in presence of N scalar particles, is done. The modification of the ADM formulation to solve the deparametrization problem of general relativity (how to recover the rest-frame instant form for G=0), is presented. The attempt to arrive at a unified description of the four interactions [with the matter being either Grassmann-valued Dirac fields or relativistic particles] based on Dirac-Bergmann theory of constraints, which is needed for the Hamiltonian formulation of both gauge theories and general relativity, motivated the study of the canonical reduction of a new formulation of tetrad gravity [1, 2, 3, 4]. This requires to look at general relativity from the canonical point of view generalizing to it all the results already obtained in the canonical study of gauge theories, since neither a complete reduction of gravity with an identification of the physical canonical degrees of freedom of the gravitational field nor a detailed study of its Hamiltonian group of 0