The loop space representation of 2+1 gravity: Physical observables, variational principles, and the issue of time
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We consider the loop space representation of Rovelli and Smolin as the starting point for the analysis of quantum gravity in 2+1 dimensions. To do so, we introduce observables directly within this representation and consider the problem of its Lagrangian formulation. The implications of this framework for the issue of time are discussed and the extension of these results to 3+1 gravity is also considered.
KeywordsVariational Principle Quantum Gravity Differential Geometry Space Representation Lagrangian Formulation
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- 1.Ashtekar, A., Husain, V., Rovelli, C., Samuel, J., and Smolin, L. (1989).Class. Quant. Grav.,6, L185.Google Scholar
- 2.Rovelli, C., and Smolin, L. (1990).Nucl. Phys. B,331, 80.Google Scholar
- 3.Carlip, S. (1990). “Observables, Gauge Invariance, and Time in 2+1 dimensional quantum gravity”, LAS preprint, LASSNS-HEP-90/41, and “Time in 2+1 Dimensional Gravity”, UCD preprint, UCDPHYS-PUB-23-90.Google Scholar
- 4.Rovelli, C. (1990). “Time in quantum gravity, an hypothesis”, Pittsburgh University preprint.Google Scholar
- 5.Brown, J. D. and Henneaux, M. (1986).Commun. Math. Phys.,104, 207.Google Scholar
- 6.Deser, S., Jackiw, R., and t'Hooft, G. (1984).Ann. Phys.,152, 220.Google Scholar