Choice of connection in loop quantum gravity
Open accessAbstract
We investigate the quantum area operator in the loop approach based on the Lorentz covariant Hamiltonian formulation of general relativity. We show that there exists a two-parameter family of Lorentz connections giving rise to Wilson lines which are eigenstates of the area operator. For each connection the area spectrum is evaluated. In particular, the results of the SU(2) approach turn out to be included in the formalism. However, only one connection from the family is a spacetime connection ensuring that the four-dimensional diffeomorphism invariance is preserved under quantization. It leads to the area spectrum independent of the Immirzi parameter. As a consequence, we conclude that the SU(2) approach must be modified according to the results obtained since it breaks one of the classical symmetries.
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- Authors
- Alexandrov, S.
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 2001-12-20
- Volume
- 65
- Issue
- 2
- Pages
- 024011
- ISSN
- 0556-2821 (ISSN-L)
- 1089-4918
- OpenAlex
- W2166798661
- Cited by
- 80
- References
- 12
- Citations by year
- 2025: 1 · 2024: 1 · 2022: 1 · 2021: 1 · 2020: 1 · 2019: 3 · 2018: 1 · 2017: 1 · 2016: 7 · 2015: 9 · 2014: 6 · 2013: 5 · 2012: 10
- FWCI
- 2.81
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- HAL (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
- loop quantum gravity, Lorentz connection, Wilson lines, area spectrum, Immirzi parameter, diffeomorphism invariance, Lorentz covariance
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