Uniqueness of the Representation in Homogeneous Isotropic LQC

Journal article

Publication Details

Author(s): Engle J, Hanusch M, Thiemann T
Journal: Communications in Mathematical Physics
Publisher: SPRINGER
Publication year: 2017
Volume: 354
Journal issue: 1
Pages range: 231-246
ISSN: 0010-3616


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.

FAU Authors / FAU Editors

Thiemann, Thomas Prof. Dr.
Chair for Theoretical Physics III (Quantum Gravity)

How to cite

Engle, J., Hanusch, M., & Thiemann, T. (2017). Uniqueness of the Representation in Homogeneous Isotropic LQC. Communications in Mathematical Physics, 354(1), 231-246. https://dx.doi.org/10.1007/s00220-017-2881-2

Engle, Jonathan, Maximilian Hanusch, and Thomas Thiemann. "Uniqueness of the Representation in Homogeneous Isotropic LQC." Communications in Mathematical Physics 354.1 (2017): 231-246.


Last updated on 2019-14-09 at 07:19