Particle models from special Jordan backgrounds and spectral triples
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866909226490658816 |
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| author | Besnard, Fabien Farnsworth, Shane |
| author_facet | Besnard, Fabien Farnsworth, Shane |
| contents | We put forward a definition for spectral triples and algebraic backgrounds based on Jordan coordinate algebras. We also propose natural and gauge-invariant bosonic configuration spaces of fluctuated Dirac operators and compute them for general, almost-associative, Jordan, coordinate algebras. We emphasize that the theory so obtained is not equivalent with usual associative noncommutative geometry, even when the coordinate algebra is the self-adjoint part of a $C^*$-algebra. In particular, in the Jordan case, the gauge fields are always unimodular, thus curing a long-standing problem in noncommutative geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_07039 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Particle models from special Jordan backgrounds and spectral triples Besnard, Fabien Farnsworth, Shane Mathematical Physics High Energy Physics - Theory Rings and Algebras We put forward a definition for spectral triples and algebraic backgrounds based on Jordan coordinate algebras. We also propose natural and gauge-invariant bosonic configuration spaces of fluctuated Dirac operators and compute them for general, almost-associative, Jordan, coordinate algebras. We emphasize that the theory so obtained is not equivalent with usual associative noncommutative geometry, even when the coordinate algebra is the self-adjoint part of a $C^*$-algebra. In particular, in the Jordan case, the gauge fields are always unimodular, thus curing a long-standing problem in noncommutative geometry. |
| title | Particle models from special Jordan backgrounds and spectral triples |
| topic | Mathematical Physics High Energy Physics - Theory Rings and Algebras |
| url | https://arxiv.org/abs/2206.07039 |