Quantizing Regge calculus
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A discretized version of canonical gravity in (3 + 1) dimensions introduced in a previous paper is further developed, introducing the Liouville form and the Poisson brackets, and studying them in detail in an explicit parametrization that shows the nature of the variables when the second class constraints are imposed. It is then shown that, even leaving aside the difficult question of imposing the first class constraints on the states, it is impossible to quantize the model directly using complex variables and leaving the second class constraints to fix the metric of the quantum Hilbert, because one cannot find a metric which makes the area variables Hermitean.
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Our expression for the proper time propagator U(T) of GR as a sum over worldsheets resembles in many ways the worldsheet sum for the projector on physical states, U_OCY, of the OCY model.
“More specifically, our expression for the proper time propagator U ( T ) of GR as a sum over worldsheets resembles in many ways the worldsheet sum [8,56] 14 for the projector on physical states, U OCY , of the OCY model.”
From “Sum over surfaces” form of loop quantum gravity (1997) · cites this paper as [56]
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References 13 · Cited by 16
Research works printed but not linked: 3
- Ashtekar 1991 A Non-perturbative Canonical Quantum Gravity notes prepared in collaboration with R Tate (Singapore: World Scientific)
- Ashtekar A and Loll R Preprint gr-qc/9405031 · arXiv
- Frölich J 1983 Preprint IHES (1992 reprinted in Non-perturbative Quantum Field Theory (Singapore: World Scientific))
- Authors
- Immirzi, G.
- Affiliations
- University of Perugia (IT)
- Corresponding author
- Immirzi, Giorgio
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 1996-09-01
- Volume
- 13
- Issue
- 9
- Pages
- 2385-2393
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W2031743224
- Cited by
- 16
- References
- 13
- Citations by year
- 2024: 1 · 2017: 1
- FWCI
- 2.09
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Classical and Quantum Gravity (publishedVersion)
- arXiv (Cornell University) (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
- Regge calculus, canonical gravity, Poisson brackets, second-class constraints, first-class constraints, quantum Hilbert space, area operator, Hermiticity, 3+1 dimensional gravity
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