Quasicoherent states of noncommutative D2-branes, Aharonov-Bohm effect and quantum Mobius strip
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917423964225536 |
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| author | Viennot, David |
| author_facet | Viennot, David |
| contents | We find an analytical formula for the quasicoherent states of 3D fuzzy spaces defined by algebras generated by bosonic creation and annihilation operators. This one is expressed in a representation onto the coherent states of the CCR algebra. Such a fuzzy space can be assimilated to a noncommutative D2-brane of the M-theory (but also as a model of a qubit in contact with a bosonic environment). We apply this formula onto a D2-brane wrapped around an axis to obtain the geometry of a noncommutative cylinder. We show that the adiabatic transport of its quasicoherent states exhibits a topological effect similar to the Aharonov-Bohm effect. We study also a D2-brane wrapped and twisted to have the geometry of a noncommutative Mobius strip. Finally we briefly present the other two examples of a noncommutative torus and of a noncommutative Klein bottle. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_07510 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quasicoherent states of noncommutative D2-branes, Aharonov-Bohm effect and quantum Mobius strip Viennot, David Mathematical Physics High Energy Physics - Theory We find an analytical formula for the quasicoherent states of 3D fuzzy spaces defined by algebras generated by bosonic creation and annihilation operators. This one is expressed in a representation onto the coherent states of the CCR algebra. Such a fuzzy space can be assimilated to a noncommutative D2-brane of the M-theory (but also as a model of a qubit in contact with a bosonic environment). We apply this formula onto a D2-brane wrapped around an axis to obtain the geometry of a noncommutative cylinder. We show that the adiabatic transport of its quasicoherent states exhibits a topological effect similar to the Aharonov-Bohm effect. We study also a D2-brane wrapped and twisted to have the geometry of a noncommutative Mobius strip. Finally we briefly present the other two examples of a noncommutative torus and of a noncommutative Klein bottle. |
| title | Quasicoherent states of noncommutative D2-branes, Aharonov-Bohm effect and quantum Mobius strip |
| topic | Mathematical Physics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2509.07510 |