The Canonical Lagrangian Approach To Three-Space General Relativity
Abstract
We study the action for the three-space formalism of General Relativity, better known as the BF\'O (Barbour--Foster--\'O Murchadha) action, which is a square-root BSW (Baierlein--Sharp--Wheeler) action. In particular, we explore the (pre)symplectic structure by pulling it back via a Legendre map to the tangent bundle of the configuration space of this action. With it we attain the canonical Lagrangian vector field which generates the gauge transformations (3-diffeomorphisms) and the true physical evolution of the system. This vector field encapsulates all the dynamics of the system. We also discuss briefly the observables and perennials for this theory. We then present a symplectic reduction of the constrained phase space.
Keywords
Cite
@article{arxiv.1209.5042,
title = {The Canonical Lagrangian Approach To Three-Space General Relativity},
author = {Vasudev Shyam and Madhavan Venkatesh},
journal= {arXiv preprint arXiv:1209.5042},
year = {2013}
}
Comments
12 pages, 4 figures, modified in accordance with reviewers' comments. Accepted for publication in General Relativity and Gravitation