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Andrew Randono is a grad student at U Texas Austin (where Steven Weinberg is, not to mention Jacques Distler). His advisor AFAIK is Richard Matzner (a Gen Rel expert at the Center for Relativity there). Randono spent the summer at Perimeter this year.

I think he has written a major paper generalizing the Kodama state. A two-part paper actually.

I put it on the links thread, but it could be useful to have a separate thread for discussion.

here are the abstracts:

http://arxiv.org/abs/gr-qc/0611073

Generalizing the Kodama State I: Construction

Andrew Randono

First part in two part series, 20 pages

The Kodama State is unique in being anexact solution to all the ordinary constraints of canonical quantum gravity that also has a well defined semi-classical interpretation as a quantum version of a classical spacetime, namely (anti)de Sitter space.However, the state is riddled with difficulties which can be tracked down to the complexification of the phase space necessary in its construction. This suggests a generalization of the state to real values of the Immirzi parameter. In this first part of a two paper series we show that one cangeneralize the state to real variables and the result is surprising in that it appears to open up an infinite class of physical states. We show that these states closely parallel the ordinary momentum eigenstates of non-relativistic quantum mechanics with the Levi-Civita curvature playing the role of the momentum. With this identification, the states inherit many of thefamiliar properties of the momentum eigenstates including delta-function normalizability. In the companion paper we will discuss the physical interpretation, CPT properties, and an interesting connection between the inner product and the Macdowell-Mansouri formulation of general relativity. "

http://arxiv.org/abs/gr-qc/0611074

Generalizing the Kodama State II: Properties and Physical Interpretation

Andrew Randono

Second paper in two part series. 18 pages

"In this second part of a two paper series we discuss the properties and physical interpretation of the generalized Kodama states. We first show that the states are the three dimensional boundary degrees of freedom of two familiar 4-dimensional topological invariants: the second Chern class and the Euler class. Using this, we show that the states have the familiar interpretation as WKB states, in this case corresponding not only to de Sitter space, but also to first order perturbations therein. In an appropriate spatial topology, the de Sitter solution has pure Chern-Simons functional form, and is the unique state in the class that is identically diffeomorphism and SU(2) gauge invariant. The q-deformed loop transform of this state yields evidence of a cosmological horizon when the deformation parameter is a root of untiy. We then discuss the behavior of the states under discrete symmetries, showing that the states violate P and T due to the presence of the Immirzi parameter, but they are CPT invariant. We conclude with an interesting connection between the physical inner product and the Macdowell Mansouri formulation of gravity."

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# Randono perfects Kodama state

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