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Universe 2016, 2(3), 18; doi:10.3390/universe2030018

Symplectic Structure of Intrinsic Time Gravity

1
Physics Department, U.S. Naval Academy, Annapolis, MD 21401, USA
2
Mathematical Sciences Department, University of South Africa, Pretoria 0002, South Africa
*
Author to whom correspondence should be addressed.
Academic Editor: Lorenzo Iorio
Received: 13 June 2016 / Revised: 4 August 2016 / Accepted: 5 August 2016 / Published: 30 August 2016
View Full-Text   |   Download PDF [249 KB, uploaded 30 August 2016]

Abstract

The Poisson structure of intrinsic time gravity is analysed. With the starting point comprising a unimodular three-metric with traceless momentum, a trace-induced anomaly results upon quantization. This leads to a revision of the choice of momentum variable to the (mixed index) traceless momentric. This latter choice unitarily implements the fundamental commutation relations, which now take on the form of an affine algebra with SU(3) Lie algebra amongst the momentric variables. The resulting relations unitarily implement tracelessness upon quantization. The associated Poisson brackets and Hamiltonian dynamics are studied. View Full-Text
Keywords: intrinsic time; quantum gravity; canonical; quantization; symmetry intrinsic time; quantum gravity; canonical; quantization; symmetry
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Ita, E.E.; Kubeka, A.S. Symplectic Structure of Intrinsic Time Gravity. Universe 2016, 2, 18.

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