Diffeomorphism covariant representations of the holonomy-flux -algebra
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Recently, Sahlmann (2002 Preprint gr-qc/0207111) proposed a new, algebraic point of view on the loop quantization. He brought up the issue of a ⋆-algebra underlying that framework, studied the algebra consisting of the fluxes and holonomies and characterized its representations. We define the diffeomorphism covariance of a representation of the Sahlmann algebra and study the diffeomorphism covariant representations. We prove they are all given by Sahlmann's decomposition into the cyclic representations of the subalgebra of the holonomies by using a single state only. The state corresponds to the natural measure defined on the space of the generalized connections. This result is a generalization of Sahlmann's result (2002 Preprint gr-qc/0207112) concerning the U (1) case.
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The only measure satisfying the condition (88) coincides with the measure defined on A by the state ω0 described in the example.
“As it was shown in [15] the only measure satisfying the above condition coincides with the measure defined on A by the state ω 0 described in the example.”
From Uniqueness of Diffeomorphism Invariant States on Holonomy–Flux Algebras (2006) · cites this paper as [15]
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- Authors
- Oko w, A., & Lewandowski, J.
- Affiliations
- Pennsylvania State University (US)
- ORCID
- Lewandowski, Jerzy
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 2003-07-22
- Volume
- 20
- Issue
- 16
- Pages
- 3543-3567
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W2020174113
- Cited by
- 58
- References
- 43
- Citations by year
- 2016: 1 · 2013: 1 · 2012: 1
- FWCI
- 9.62
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Classical and Quantum Gravity (publishedVersion)
- arXiv (Cornell University) (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 › Mathematics › Mathematical Physics › Advanced Operator Algebra Research
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Keywords
- general covariance, loop quantum gravity, cyclic representations, generalized connections, quantum connection
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