New loop representations for 21 gravity
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Since the gauge group underlying (2+1)-dimensional general relativity is non-compact, certain difficulties arise in the passage from the connection to the loop representations. It is shown that these problems can be handled by appropriately choosing the measure that features in the definition of the loop transform. Thus, `old-fashioned' loop representations---based on ordinary loops---do exist. In the case when the spatial topology is that of a 2-torus, these can be constructed explicitly; all quantum states can be represented as functions of (homotopy classes of) loops and the scalar product and the action of the basic observables can be given directly in terms of loops.
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A second possibility is to change the integration measure in the loop transform to make various integrals converge better.
“A second possibility is to change the integration measure in the loop transform to make various integrals converge better [30].”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [30]
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2 + 1 dimensional gravity as an exactly soluble system
Witten, E. (1988) · Nuclear Physics B · doi:10.1016/0550-3213(88)90143-5 · Cited by 2,562 · see citing works
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Quantum gravity and Regge calculus
Immirzi, G. (1997) · Nuclear Physics B - Proceedings Supplements · doi:10.1016/s0920-5632(97)00354-x · Cited by 287 · see citing works
Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe
Carlip, S. (2005) · Living Reviews in Relativity · doi:10.12942/lrr-2005-1 · Cited by 172 · see citing works
- Authors
- Ashtekar, A., & Loll, R.
- Affiliations
- Pennsylvania State University (US)
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 1994-10-01
- Volume
- 11
- Issue
- 10
- Pages
- 2417-2434
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W2047303640
- Cited by
- 24
- References
- 1
- Citations by year
- 2020: 1 · 2013: 1 · 2012: 1
- FWCI
- 3.32
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Classical and Quantum Gravity (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation
- Pennsylvania State University
- Deutsche Forschungsgemeinschaft
- 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
- loop representation, quantum states, quantum gravity
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