Spectral Torsion
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866909291872518144 |
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| author | Dąbrowski, Ludwik Sitarz, Andrzej Zalecki, Paweł |
| author_facet | Dąbrowski, Ludwik Sitarz, Andrzej Zalecki, Paweł |
| contents | We introduce a trilinear functional of differential one-forms for a finitely summable regular spectral triple with a noncommutative residue. We demonstrate that for a canonical spectral triple over a closed spin manifold it recovers the torsion of the linear connection. We examine several spectral triples, including Hodge-de\,Rham, Einstein-Yang-Mills, almost-commutative two-sheeted space, conformally rescaled noncommutative tori, and quantum $SU(2)$ group, showing that the third one has a nonvanishing torsion if nontrivially coupled. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_01644 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Spectral Torsion Dąbrowski, Ludwik Sitarz, Andrzej Zalecki, Paweł Quantum Algebra General Relativity and Quantum Cosmology Mathematical Physics Differential Geometry Spectral Theory 58B34, 46L87, 58J42, 83C65, 58J50 We introduce a trilinear functional of differential one-forms for a finitely summable regular spectral triple with a noncommutative residue. We demonstrate that for a canonical spectral triple over a closed spin manifold it recovers the torsion of the linear connection. We examine several spectral triples, including Hodge-de\,Rham, Einstein-Yang-Mills, almost-commutative two-sheeted space, conformally rescaled noncommutative tori, and quantum $SU(2)$ group, showing that the third one has a nonvanishing torsion if nontrivially coupled. |
| title | Spectral Torsion |
| topic | Quantum Algebra General Relativity and Quantum Cosmology Mathematical Physics Differential Geometry Spectral Theory 58B34, 46L87, 58J42, 83C65, 58J50 |
| url | https://arxiv.org/abs/2308.01644 |