Gravity: a gauge theory perspective

TL;DR

This paper explores gravity as a gauge theory, emphasizing a covariant Hamiltonian approach that yields covariant expressions for quasi-local energy, and discusses the role of torsion and the Poincaré gauge group in gravitational dynamics.

Contribution

It introduces a covariant Hamiltonian formulation of gravity as a Poincaré gauge theory, providing new covariant boundary terms for energy and momentum.

Findings

Covariant Hamiltonian formulation of gravity developed.

Covariant expressions for quasi-local energy, momentum, and angular momentum derived.

Torsion may have significant cosmological effects without being locally noticeable.

Abstract

The evolution of a generally covariant theory is under-determined. One hundred years ago such dynamics had never before been considered; its ramifications were perplexing, its future important role for all the fundamental interactions under the name gauge principle could not be foreseen. We recount some history regarding Einstein, Hilbert, Klein and Noether and the novel features of gravitational energy that led to Noether's two theorems. Under-determined evolution is best revealed in the Hamiltonian formulation. We developed a covariant Hamiltonian formulation. The Hamiltonian boundary term gives covariant expressions for the quasi-local energy, momentum and angular momentum. Gravity can be considered as a gauge theory of the local Poincar\'e group. The dynamical potentials of the Poincar\'e gauge theory of gravity are the frame and the connection. The spacetime geometry has in general both curvature and torsion. Torsion naturally couples to spin; it could have a significant magnitude and yet not be noticed, except on a cosmological scale where it could have significant effects.