Spectral Metric and Einstein Functionals for Hodge-Dirac operator
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866910571304058880 |
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| author | Dąbrowski, Ludwik Zalecki, Paweł Sitarz, Andrzej |
| author_facet | Dąbrowski, Ludwik Zalecki, Paweł Sitarz, Andrzej |
| contents | We examine the metric and Einstein bilinear functionals of differential forms introduced in Adv.Math.,Vol.427,(2023)1091286, for Hodge-Dirac operator $d+δ$ on an oriented even-dimensional Riemannian manifold. We show that they reproduce these functionals for the canonical Dirac operator on a spin manifold up to a numerical factor. Furthermore, we demonstrate that the associated spectral triple is spectrally closed, which implies that it is torsion-free. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2307_14877 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Spectral Metric and Einstein Functionals for Hodge-Dirac operator Dąbrowski, Ludwik Zalecki, Paweł Sitarz, Andrzej Differential Geometry Mathematical Physics Quantum Algebra Spectral Theory 58J50, 46L87, 58B34 We examine the metric and Einstein bilinear functionals of differential forms introduced in Adv.Math.,Vol.427,(2023)1091286, for Hodge-Dirac operator $d+δ$ on an oriented even-dimensional Riemannian manifold. We show that they reproduce these functionals for the canonical Dirac operator on a spin manifold up to a numerical factor. Furthermore, we demonstrate that the associated spectral triple is spectrally closed, which implies that it is torsion-free. |
| title | Spectral Metric and Einstein Functionals for Hodge-Dirac operator |
| topic | Differential Geometry Mathematical Physics Quantum Algebra Spectral Theory 58J50, 46L87, 58B34 |
| url | https://arxiv.org/abs/2307.14877 |