Pseudo-Riemannian spectral triples and the harmonic oscillator

Authors

Koen van den Dungen, Australian National UniversityFollow
Mario Paschke, Australian National University
Adam C. Rennie, University of WollongongFollow

RIS ID

79660

Publication Details

van den Dungen, K. L., Paschke, M. & Rennie, A. C. (2013). Pseudo-Riemannian spectral triples and the harmonic oscillator. Journal of Geometry and Physics, 73 (November), 37-55.

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 K-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. 2013 Elsevier B.V.