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2012

On the Uniqueness of Kinematics of Loop Quantum Cosmology

Ashtekar, Abhay, Campiglia, Miguel

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The holonomy-flux algebra $\A$ of loop quantum gravity is known to admit a natural representation that is uniquely singled out by the requirement of covariance under spatial diffeomorphisms.

In the cosmological context, the requirement of spatial homogeneity naturally reduces $\A$ to a much smaller algebra, $\A_{\rm Red}$, used in loop quantum cosmology.
In Bianchi I models, it is shown that the requirement of covariance under \emph{residual} diffeomorphism symmetries again uniquely selects the representation of $\A_{\rm Red}$ that has been commonly used.
We discuss the close parallel between the two uniqueness results and also point out a difference.

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Built on

Gel’fand I M and Naimark M A, 1943 On the embedding of normed rings into the ring of operators in Hilbert space, Mat. Sobrn. 12, [54]
1947
Earlier work this paper cites.
Baez J C 1994 Generalized measures in gauge theory Lett. Math. Phys
1994
Earlier work this paper cites.
Ashtekar A and Lewandowski J 1994 Representation theory of analytic holonomy algebras, in Knots and Quantum Gravity
1995
Earlier work this paper cites.
Ashtekar A and Isham C J 1992 Representation of the holonomy algebras of gravity and non-Abelian gauge theories Class. Quant. Grav
1998
Earlier work this paper cites.

Similar

A. Ashtekar, M. Bojowald and J. Lewandowski, Mathematical structure of loop quantum cosmology. Adv. Theo. Math. Phys. 7
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Ashtekar A and Lewandowski A, 2004 Background independent quantum gravity: A status report, Class. Quant. Grav. 21
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Lewandowski J, Okołów A, Sahlmann H, Thiemann T 2006 Uniqueness of the diffeomorphism invariant state on the quantum holonomy-flux algebras, Comm. Math. Phys. 267
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Fleishchack C, 2009 Representations of the Weyl algebra in quantum geometry, Commun. Math. Phys. 285
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Then

Ashtekar A and Wilson-Ewing E, 2009 Loop quantum cosmology of Bianchi type I models, Phys. Rev. D 79
2009
Later among the works it cites.
Ashtekar A and Singh P, 2009 Loop Quantum Cosmology: A Status Report, Class. Quant. Grav. 28
2009
Later among the works it cites.
Ashtekar A, Campiglia M and Henderson A 2011 (unpublished notes)
2011
Later among the works it cites.

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