Finite spectral triples for the fuzzy torus
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2019
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| _version_ | 1866929567607816192 |
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| author | Barrett, John W. Gaunt, James |
| author_facet | Barrett, John W. Gaunt, James |
| contents | Finite real spectral triples are defined to characterise the non-commutative geometry of a fuzzy torus. The geometries are the non-commutative analogues of flat tori with moduli determined by integer parameters. Each of these geometries has four different Dirac operators, corresponding to the four unique spin structures on a torus. The spectrum of the Dirac operator is calculated. It is given by replacing integers with their quantum integer analogues in the spectrum of the corresponding commutative torus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1908_06796 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Finite spectral triples for the fuzzy torus Barrett, John W. Gaunt, James Quantum Algebra General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics 58B34, 81T75 Finite real spectral triples are defined to characterise the non-commutative geometry of a fuzzy torus. The geometries are the non-commutative analogues of flat tori with moduli determined by integer parameters. Each of these geometries has four different Dirac operators, corresponding to the four unique spin structures on a torus. The spectrum of the Dirac operator is calculated. It is given by replacing integers with their quantum integer analogues in the spectrum of the corresponding commutative torus. |
| title | Finite spectral triples for the fuzzy torus |
| topic | Quantum Algebra General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics 58B34, 81T75 |
| url | https://arxiv.org/abs/1908.06796 |