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Uniqueness of the Representation in Homogeneous Isotropic LQC

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A Correction to this article was published on 30 July 2018

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Abstract

We show that the standard representation of homogeneous isotropic loop quantum cosmology (LQC) is the GNS-representation that corresponds to the unique state on the reduced quantum holonomy-flux *-algebra that is invariant under residual diffeomorphisms—both when the standard algebra is used as well as when one uses the extended algebra proposed by Fleischhack. More precisely, we find that in both situations the GNS-Hilbert spaces coincide, and that in the Fleischhack case the additional algebra elements are just mapped to zero operators. In order for the residual diffeomorphisms to have a well-defined action on the quantum algebra, we have let them act on the fiducial cell as well as on the dynamical variables, thereby recovering covariance. Consistency with Ashtekar and Campilgia in the Bianchi case is also shown.

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  • 30 July 2018

    We correct some oversights contained in [1].

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Authors and Affiliations

  1. Department of Physics, Florida Atlantic University, 777 Glades Road, Boca Raton, FL, 33431, USA

    Jonathan Engle & Maximilian Hanusch

  2. Institute for Quantum Gravity, Friedrich-Alexander University Erlangen-Nürnburg, Staudstraße 7, 91058, Erlangen, Germany

    Jonathan Engle & Thomas Thiemann

Authors
  1. Jonathan Engle
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  2. Maximilian Hanusch
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  3. Thomas Thiemann
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Corresponding author

Correspondence to Maximilian Hanusch.

Additional information

Communicated by Y. Kawahigashi

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Engle, J., Hanusch, M. & Thiemann, T. Uniqueness of the Representation in Homogeneous Isotropic LQC. Commun. Math. Phys. 354, 231–246 (2017). https://doi.org/10.1007/s00220-017-2881-2

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  • DOI: https://doi.org/10.1007/s00220-017-2881-2

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