Astronomy and Astrophysics – Astrophysics
Scientific paper
Nov 1999
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999aipc..493..233s&link_type=abstract
Eighth Canadian conference on general relativity and relativistic astrophysics. AIP Conference Proceedings, Volume 493, pp. 233
Astronomy and Astrophysics
Astrophysics
2
Covariant And Sum-Over-Histories Quantization, Gravity In More Than Four Dimensions, Kaluza-Klein Theory, Unified Field Theories, Alternative Theories Of Gravity
Scientific paper
It is well known that in four or more dimensions, there exist exotic manifolds; manifolds that are homeomorphic but not diffeomorphic to each other. This is in contrast to the uniqueness of the differentiable structure on manifolds in one, two and three dimensions. As exotic manifolds are not diffeomorphic, one can argue that functional integrals for gravity should include a sum over not only physically distinct geometries and topologies but also inequivalent differentiable structures. But can the inclusion of exotic manifolds in such sums make a significant contribution to these quantum amplitudes? In a word, yes. Simply connected exotic Einstein manifolds with positive curvature exist in seven dimensions. Their metrics are found numerically; they are shown to have volumes of the same order of magnitude. Their contribution to the semiclassical evaluation of the partition function for Euclidean quantum gravity in seven dimensions is evaluated and found to be nontrivial. Consequently, inequivalent differentiable structures should be included in the formulation of sums over histories for quantum gravity.
Schleich Kristin
Witt Donald M.
No associations
LandOfFree
Exotic spaces and 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 Exotic spaces and quantum gravity, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Exotic spaces and quantum gravity will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-1283904