# Non-compact spectral triples with finite volume

@article{Wulkenhaar2009NoncompactST, title={Non-compact spectral triples with finite volume}, author={Raimar Wulkenhaar}, journal={arXiv: High Energy Physics - Theory}, year={2009} }

In order to extend the spectral action principle to non-compact spaces, we propose a framework for spectral triples where the algebra may be non-unital but the resolvent of the Dirac operator remains compact. We show that an example is given by the supersymmetric harmonic oscillator which, interestingly, provides two different Dirac operators. This leads to two different representations of the volume form in the Hilbert space, and only their product is the grading operator. The index of the…

## 19 Citations

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