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Uniqueness of the Representation in Homogeneous Isotropic LQC

Jun 28
Group Seminar
4:00 pm o'clock to 6:00 pm o'clock
Prof. Jonathan Engle (Florida Atlantic University)
SR 02.729

We show that the standard representation of homogeneous isotropic loop quantum cosmology (LQC) used in the literature is the GNS-representation associated to the unique state on the reduced quantum holonomy-flux ∗-algebra that is invariant under residual diffeomorphisms — *both* when the standard algebra with holonomies along only straight edges is used, as well as when one extends the algebra to include curved edges (a la Fleischhack). 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.