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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2604.19549 |
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| _version_ | 1866913051283816448 |
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| author | Barrett, John W. Burridge, Joseph |
| author_facet | Barrett, John W. Burridge, Joseph |
| contents | The product of a non-commutative matrix spectral triple with a simple two-dimensional internal space is considered. This is interpreted as a non-commutative spacetime that contains one charged Dirac fermion and its antiparticle. The inner fluctuations of a vacuum Dirac operator are calculated, using the standard technique of Connes' one-forms. This results in the non-commutative analogue of a gauge field, as expected, and also fluctuations of the spacetime geometry. In addition, the fluctuations include a derivative operator that depends on the particle charge. The integral over the fermions in the model is calculated, leading to some novel induced bosonic terms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_19549 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fuzzy Geometries with an Internal Space Barrett, John W. Burridge, Joseph Mathematical Physics 58B34 The product of a non-commutative matrix spectral triple with a simple two-dimensional internal space is considered. This is interpreted as a non-commutative spacetime that contains one charged Dirac fermion and its antiparticle. The inner fluctuations of a vacuum Dirac operator are calculated, using the standard technique of Connes' one-forms. This results in the non-commutative analogue of a gauge field, as expected, and also fluctuations of the spacetime geometry. In addition, the fluctuations include a derivative operator that depends on the particle charge. The integral over the fermions in the model is calculated, leading to some novel induced bosonic terms. |
| title | Fuzzy Geometries with an Internal Space |
| topic | Mathematical Physics 58B34 |
| url | https://arxiv.org/abs/2604.19549 |