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Pseudo-Riemannian spectral triples and the harmonic oscillator

Journal Article


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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.

Authors


  •   van den Dungen, Koen L. (external author)
  •   Paschke, Mario (external author)
  •   Rennie, Adam C.

Publication Date


  • 2013

Citation


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

Scopus Eid


  • 2-s2.0-84878802302

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=2337&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/1328

Number Of Pages


  • 18

Start Page


  • 37

End Page


  • 55

Volume


  • 73

Issue


  • November

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.

Authors


  •   van den Dungen, Koen L. (external author)
  •   Paschke, Mario (external author)
  •   Rennie, Adam C.

Publication Date


  • 2013

Citation


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

Scopus Eid


  • 2-s2.0-84878802302

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=2337&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/1328

Number Of Pages


  • 18

Start Page


  • 37

End Page


  • 55

Volume


  • 73

Issue


  • November