The volume operator in covariant quantum gravity
Open accessAbstract
A covariant spin-foam formulation of quantum gravity has been recently developed, characterized by a kinematics which appears to match well the one of canonical loop quantum gravity. In particular, the geometrical observable giving the area of a surface has been shown to be the same as the one in loop quantum gravity. Here we discuss the volume observable. We derive the volume operator in the covariant theory, and show that it matches the one of loop quantum gravity, as does the area. We also reconsider the implementation of the constraints that defines the model: we derive in a simple way the boundary Hilbert space of the theory from a suitable form of the classical constraints, and show directly that all constraints vanish weakly on this space.
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In the Riemannian Gupta-Bleuler approach with γ < 1, restricting Spin(4) representations to the maximum-weight component j = j+ + j− satisfies the relevant condition.
“Case γ < 1: Following [142], in this case one restricts the Spin(4) representations to 130 which amounts to choosing the maximum weight component j = j+ + j− in the expansion (182). Simple algebra shows that condition (188) is met.”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [142]
Geometric operators such as volume and area defined in the covariant context coincide with the corresponding operators in the canonical formulation.
“Moreover, geometric operators such as volume and area defined in the covariant context are shown to coincide with the corresponding operators defined in the canonical formulation [141, 142].”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [142]
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- Authors
- Ding, Y., & Rovelli, C.
- ORCID
- Ding, You
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 2010-06-29
- Volume
- 27
- Issue
- 16
- Pages
- 165003
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W2156604430
- Cited by
- 23
- References
- 33
- Citations by year
- 2025: 1 · 2024: 1 · 2022: 2 · 2021: 3 · 2019: 1 · 2017: 1 · 2014: 2 · 2013: 2 · 2012: 3
- FWCI
- 2.72
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Classical and Quantum Gravity (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- HAL AMU (submittedVersion, other-oa)
- Trinity's Access to Research Output (TARA) (Trinity College Dublin) (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
- spin foam models, volume operator, loop quantum gravity, area operator, constraints, soft constraints, kinematics
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