Presymplectic Geometry and the Problem of Time. Part 1

2012/09/25 by Vasudev Shyam, Shyam, Vasudev, B. Ramachandra +2 · 2 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Homotopy and Cohomology in Algebraic Topology #Noncommutative and Quantum Gravity Theories #gr-qc

paper · pdf · doi:10.48550/arxiv.1209.5547

11 pages, no figures

arxiv created 2012/10/02 · arxiv updated 2012/10/03

Abstract

An effective mathematical framework based on Presymplectic Geometry for dealing with the "phase space picture" of timeless dynamics in General Relativity is presented. In General Relativity, the presence of the scalar Hamiltonian constraint which vanishes leads to the problem of time, which can be solved, up to an extent by adopting a timeless formalism. This has been done by Carlo Rovelli and Julian Barbour et al. In this paper we present a phase space reformulation of Barbour's theory. The Presymplectic dynamics of general totally constrained, reparametrization invariant theories is developed, then applied to Jacobi mechanics, relational particle mechanics and the dynamics of the free relativistic particle.

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• On the Geometric Quantization of Canonical Gravity
• Presymplectic Geometry And The Problem Of Time. Part 2

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