Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1898565 | Journal of Geometry and Physics | 2013 | 19 Pages |
Abstract
We define pseudo-Riemannian spectral triples, an analytic context broad enough to encompass a spectral description of a wide class of pseudo-Riemannian manifolds, as well as their noncommutative generalisations. Our main theorem shows that to each pseudo-Riemannian spectral triple we can associate a genuine spectral triple, and so a KK-homology class. With some additional assumptions we can then apply the local index theorem. We give a range of examples and some applications. The example of the harmonic oscillator in particular shows that our main theorem applies to much more than just classical pseudo-Riemannian manifolds.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Koen van den Dungen, Mario Paschke, Adam Rennie,