Oxidation, Reduction and Semi-Classical Limit for Quantum Matrix Geometries
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866910366460542976 |
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| author | Felder, Laura O. Steinacker, Harold C. |
| author_facet | Felder, Laura O. Steinacker, Harold C. |
| contents | Matrix configurations define noncommutative spaces endowed with extra structure including a generalized Laplace operator, and hence a metric structure. Made dynamical via matrix models, they describe rich physical systems including noncommutative gauge theory and emergent gravity. Refining the construction in [1], we construct a semi-classical limit through an immersed submanifold of complex projective space based on quasi-coherent states. We observe the phenomenon of oxidation, where the resulting semi-classical space acquires spurious extra dimensions. We propose to remove this artifact by passing to a leaf of a carefully chosen foliation, which allows to extract the geometrical content of the noncommutative spaces. This is demonstrated numerically via multiple examples. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2306_10771 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Oxidation, Reduction and Semi-Classical Limit for Quantum Matrix Geometries Felder, Laura O. Steinacker, Harold C. High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics Matrix configurations define noncommutative spaces endowed with extra structure including a generalized Laplace operator, and hence a metric structure. Made dynamical via matrix models, they describe rich physical systems including noncommutative gauge theory and emergent gravity. Refining the construction in [1], we construct a semi-classical limit through an immersed submanifold of complex projective space based on quasi-coherent states. We observe the phenomenon of oxidation, where the resulting semi-classical space acquires spurious extra dimensions. We propose to remove this artifact by passing to a leaf of a carefully chosen foliation, which allows to extract the geometrical content of the noncommutative spaces. This is demonstrated numerically via multiple examples. |
| title | Oxidation, Reduction and Semi-Classical Limit for Quantum Matrix Geometries |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics |
| url | https://arxiv.org/abs/2306.10771 |