Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2000-03-30
Phys.Rev. D62 (2000) 084005
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Latex, 30 pages, 1 figure, to appear in Phys. Rev. D
Scientific paper
10.1103/PhysRevD.62.084005
We investigate a triad representation of the Chern-Simons state of quantum gravity with a non-vanishing cosmological constant. It is shown that the Chern-Simons state, which is a well-known exact wavefunctional within the Ashtekar theory, can be transformed to the real triad representation by means of a suitably generalized Fourier transformation, yielding a complex integral representation for the corresponding state in the triad variables. It is found that topologically inequivalent choices for the complex integration contour give rise to linearly independent wavefunctionals in the triad representation, which all arise from the one Chern-Simons state in the Ashtekar variables. For a suitable choice of the normalization factor, these states turn out to be gauge-invariant under arbitrary, even topologically non-trivial gauge-transformations. Explicit analytical expressions for the wavefunctionals in the triad representation can be obtained in several interesting asymptotic parameter regimes, and the associated semiclassical 4-geometries are discussed. In restriction to Bianchi-type homogeneous 3-metrics, we compare our results with earlier discussions of homogeneous cosmological models. Moreover, we define an inner product on the Hilbert space of quantum gravity, and choose a natural gauge-condition fixing the time-gauge. With respect to this particular inner product, the Chern-Simons state of quantum gravity turns out to be a non-normalizable wavefunctional.
Graham Robert
Paternoga Robert
No associations
LandOfFree
Triad representation of the Chern-Simons state in quantum gravity does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Triad representation of the Chern-Simons state in quantum gravity, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Triad representation of the Chern-Simons state in quantum gravity will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-201666