A note on the foundation of relativistic mechanics. II: Covariant hamiltonian general relativity

TL;DR

This paper presents a simple, covariant Hamiltonian formulation of general relativity that is independent of spacetime coordinates, facilitating a clearer physical interpretation and potential applications in loop quantum gravity and spin foam models.

Contribution

It introduces a manifestly covariant Hamiltonian approach to general relativity that is defined over a finite-dimensional space and aligns with Toller's reference system transformations.

Findings

Formulation is 4D generally covariant and coordinate-independent.

Provides a physical interpretation for spin network transition amplitudes.

Applicable to loop quantum gravity and spin foam models.

Abstract

I illustrate a simple hamiltonian formulation of general relativity, derived from the work of Esposito, Gionti and Stornaiolo, which is manifestly 4d generally covariant and is defined over a finite dimensional space. The spacetime coordinates drop out of the formalism, reflecting the fact that they are not related to observability. The formulation can be interpreted in terms of Toller's reference system transformations, and provides a physical interpretation for the spinnetwork to spinnetwork transition amplitudes computable in principle in loop quantum gravity and in the spin foam models.