The N-body Problem in Tetrad Gravity: a First Step towards the Unified Description of the Four Interactions

TL;DR

This paper introduces a new formulation of tetrad gravity, extending the canonical reduction to include N scalar particles and addressing the deparametrization problem in general relativity.

Contribution

It presents a novel tetrad gravity formulation with canonical reduction, incorporating N scalar particles and modifying the ADM approach to solve deparametrization issues.

Findings

Canonical reduction of tetrad gravity with N scalar particles

Modified ADM formulation for deparametrization

Framework towards unifying the four fundamental interactions

Abstract

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.