Quantum constraints, Dirac observables and evolution: group averaging versus the Schrödinger picture in LQC
Open accessAbstract
A general quantum constraint of the form (realized in particular in loop quantum cosmology models) is studied. Group averaging is applied to define the Hilbert space of solutions and the relational Dirac observables. Two cases are considered. In the first case, the spectrum of the operator is assumed to be discrete. The quantum theory defined by the constraint takes the form of a Schrödinger-like quantum mechanics with a generalized Hamiltonian . In the second case, the spectrum is absolutely continuous and some peculiar asymptotic properties of the eigenfunctions are assumed. The resulting Hilbert space and the dynamics are characterized by a continuous family of the Schrödinger-like quantum theories. However, the relational observables mix different members of the family. Our assumptions are motivated by new loop quantum cosmology models of quantum FRW spacetime. The two cases considered in this paper correspond to the negative and positive cosmological constant, respectively. Our results should also be applicable in many other general relativistic contexts.
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The EPRL amplitudes can be generalized to arbitrary complexes with boundaries given by graphs with nodes of arbitrary valence.
“as in BF theory, the EPRL amplitudes can be generalized to arbitrary complexes with boundaries given by graphs with nodes of arbitrary valence. The extension of the model to arbitrary complexes was first studied in [237, 236] and has been revisited in [140].”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [237]
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- Authors
- Kamiński, W., Lewandowski, J., & Pawłowski, T.
- Affiliations
- University of Warsaw (PL)
- Instituto de Estructura de la Materia (ES)
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 2009-12-08
- Volume
- 26
- Issue
- 24
- Pages
- 245016
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W2003533681
- Cited by
- 46
- References
- 37
- Citations by year
- 2026: 1 · 2025: 1 · 2024: 1 · 2023: 2 · 2021: 2 · 2020: 1 · 2019: 2 · 2018: 2 · 2017: 2 · 2016: 3 · 2015: 2 · 2014: 3 · 2013: 7 · 2012: 7
- FWCI
- 3.89
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.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 › Mathematics › Mathematical Physics › Advanced Operator Algebra Research
- Keywords
- quantum constraints, loop quantum cosmology, group averaging, Dirac observables, relational observables, Schrödinger picture, generalized Hamiltonian, discrete spectrum, absolutely continuous spectrum, FLRW spacetime, cosmological constant, quantum gravity
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