Reduced Yang model and noncommutative geometry of curved spacetime
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912300664881152 |
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| author | Meljanac, S. Mignemi, S. |
| author_facet | Meljanac, S. Mignemi, S. |
| contents | The Yang model describes a noncommutative geometry in a curved spacetime by means of an orthogonal algebra $o(1,5)$, whose 15 generators are identified with phase space variables and Lorentz generators together with an additional scalar generator. In this paper we show that it is possible to define a nonlinear algebra with the same structure, but with only 14 generators, that better fits in phase space. The fifteenth generator of the Yang algebra can then be written as a function of the squares of the others.
As a simple application, we also consider the problem of the quantum harmonic oscillator in this theory, calculating the energy spectrum in the one- and three-dimensional nonrelativistic versions of the model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_23146 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reduced Yang model and noncommutative geometry of curved spacetime Meljanac, S. Mignemi, S. High Energy Physics - Theory Mathematical Physics The Yang model describes a noncommutative geometry in a curved spacetime by means of an orthogonal algebra $o(1,5)$, whose 15 generators are identified with phase space variables and Lorentz generators together with an additional scalar generator. In this paper we show that it is possible to define a nonlinear algebra with the same structure, but with only 14 generators, that better fits in phase space. The fifteenth generator of the Yang algebra can then be written as a function of the squares of the others. As a simple application, we also consider the problem of the quantum harmonic oscillator in this theory, calculating the energy spectrum in the one- and three-dimensional nonrelativistic versions of the model. |
| title | Reduced Yang model and noncommutative geometry of curved spacetime |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2503.23146 |