Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2005-11-08
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Talk given at SWH60 birthday meeting, Cambridge, England, January 2002. Published in "The future of theoretical physics and co
Scientific paper
The canonical approach to Riemannian quantum gravity is reviewed with reference to local supersymmetry, to the classical boundary-value problem arising from the Hartle-Hawking quantum state, and particularly for (anti-)self-dual geometries. Two examples of the boundary-value problem for the Einstein equations, possibly with a cosmological constant \Lambda, are treated, both of Bianchi-IX type. These close smoothly in the interior with a NUT or a BOLT. The Hamiltonian approach to general relativity is described using Ashtekar variables; for non-zero \Lambda and anti-self-dual Weyl tensor, the classical solution corresponds, with the most naive choice of boundary data, to the Chern-Simons functional of the boundary data, the classical action being I_{CS}. Hence, one is led to the corresponding quantum states exp(\pm I_{CS}). Apparently, the classical solutions have the undesirable feature that, in general, the resulting Riemannian classical geometry, arising from the Hamilton-Jacobi equation, does not close smoothly in the interior. The canonical quantum theory of supergravity is also described, and may lead to very streamlined (finite) calculations of loop amplitudes for N=1 supergravity with gauged supermatter. If one uses Ashtekar/Jacobson variables for canonical supergravity, then again (for \Lambda\neq 0) one arrives at a (supersymmetric) Chern-Simons action and quantum state in the (anti-)self-dual case.
No associations
LandOfFree
What local supersymmetry can do for quantum cosmology 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 What local supersymmetry can do for quantum cosmology, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and What local supersymmetry can do for quantum cosmology will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-293659