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Global constants in (2+1)-dimensional gravity

J E Nelson

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The extended conformal algebra so(2, 3) of global, quantum, constants of motion in (2+1)-dimensional gravity with topology R × T2 and negative cosmological constant is reviewed. It is shown that the ten global constants form a complete set by expressing them in terms of two commuting spinors and the Dirac γ matrices. The spinor components are the globally constant holonomy parameters, and their respective spinor norms are their quantum commutators.


PACS

04.60.Kz Lower dimensional models; minisuperspace models

02.10.Yn Matrix theory

04.60.Ds Canonical quantization

02.40.Re Algebraic topology

98.80.Es Observational cosmology (including Hubble constant, distance scale, cosmological constant, early Universe, etc)

02.20.Uw Quantum groups

MSC

83C45 Quantization of the gravitational field

81Q70 Differential-geometric methods, including holonomy, Berry and Hannay phases, etc.

20G42 Quantum groups (quantized function algebras) and their representations (See also 16W35, 17B37, 81R50)

83F05 Cosmology

Subjects

Mathematical physics

Gravitation and cosmology

Astrophysics and astroparticles

Dates

Issue 3 (7 February 2004)

Received 21 October 2003

Published 13 January 2004



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