Loop quantum cosmology: III. Wheeler-DeWitt operators
Open accessAbstract
Within the framework of loop quantum cosmology anomaly-free quantizations of the Hamiltonian constraint for Bianchi class A, locally rotationally symmetric and isotropic models are given. Basic ideas of the construction in (non-symmetric) loop quantum gravity can be used, but there are also further inputs because the special structure of symmetric models has to be respected by operators. In particular, the basic building blocks of the homogeneous models are point holonomies rather than holonomies necessitating a new regularization procedure. In this respect, our construction is also applicable for other (non-homogeneous) symmetric models, e.g. the spherically symmetric one.
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The evolution equation is not a differential equation in time, but a difference equation manifesting the discreteness of time.
“This implies another difference, namely that the evolution equation is not a differential equation in time, but a difference equation manifesting the discreteness of time [13].”
From Absence of a Singularity in Loop Quantum Cosmology (2001) · cites this paper as [13]
Discrete geometry implies that eigenvalues of p are discrete, whence time evolution is now discrete.
“Furthermore, discrete geometry imples that eigenvalues of p are discrerte, whence time evolution is now discrete (see [13] for details).”
From Absence of a Singularity in Loop Quantum Cosmology (2001) · cites this paper as [13]
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Cites
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Self-citation
- Authors
- Bojowald, M.
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 2001-02-27
- Volume
- 18
- Issue
- 6
- Pages
- 1055-1069
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W1988029030
- Cited by
- 83
- References
- 8
- Citations by year
- 2025: 1 · 2023: 4 · 2022: 2 · 2020: 1 · 2017: 2 · 2016: 3 · 2015: 2 · 2014: 1 · 2013: 2 · 2012: 6
- FWCI
- 5.84
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Classical and Quantum Gravity (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- RWTH Publications (RWTH Aachen) (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 › Cosmology and Gravitation Theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Keywords
- loop quantum cosmology, Wheeler-DeWitt equation, Hamiltonian constraint, isotropic model, spherically symmetric models, quantum gravity
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