THE CONSTRAINT ALGEBRA OF QUANTUM GRAVITY IN THE LOOP REPRESENTATION
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We study the algebra of constraints of quantum gravity in the loop representation based on Ashtekar’s new variables. We show by direct computation that the quantum commutator algebra reproduces the classical Poisson bracket one, in the limit in which regulators are removed. The calculation illustrates the use of several computational techniques for the loop representation.
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If the commutator vanishes only in the limit ε→0, then the theory still has an anomaly, in the sense that its classical limit has non-vanishing Poisson brackets on the diffeomorphism constraint surface.
“if the commutator only vanishes in the limit → 0 then one still has an anomaly in the sense that the classical limit of that theory has non-vanishing Poisson brackets on the constraint surface defined by the diffeomorphism constraint.”
From Quantum spin dynamics (QSD) (1998) · cites this paper as [25]
The operator only annihilates Diff but not the extensions * discussed in [24].
“in view of [25] it is clear that it only annihilates Diff but not any of the extensions * discussed in [24].”
From Quantum spin dynamics (QSD) (1998) · cites this paper as [25]
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- [10]A.Garat, M.Sc. Thesis, Universidad de la Rep´ ublica (unpublished) (1994).
- Authors
- GAMBINI, R., GARAT, A., & PULLIN, J.
- Affiliations
- Universidad de la República de Uruguay (UY)
- University of Utah (US)
- Pennsylvania State University (US)
- Venue
- International Journal of Modern Physics D
- Publisher
- World Scientific Pub Co Pte Lt
- Published
- 1995-10
- Volume
- 04
- Issue
- 05
- Pages
- 589-616
- ISSN
- 0218-2718 (ISSN-L)
- 1793-6594
- OpenAlex
- W2084294237
- Cited by
- 19
- References
- 0
- Citations by year
- 2024: 1 · 2023: 1 · 2022: 2
- FWCI
- 2.91
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- International Journal of Modern Physics D (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Civil War Book Review (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Keywords
- quantum gravity, loop representation, Ashtekar variables, constraint algebra, Poisson brackets, canonical quantization, loop quantum gravity
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