Poisson Gauge Theories in Three Dimensions: Exact Solutions and Conservation Laws
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866910125795573760 |
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| author | Sharapov, Alexey Shcherbatov, David |
| author_facet | Sharapov, Alexey Shcherbatov, David |
| contents | We investigate Maxwell-Chern-Simons theory on a three-dimensional noncommutative spacetime endowed with a constant spacelike Poisson structure. By exploiting the residual rotational symmetry, we construct exact classical solutions corresponding to pointlike electric and magnetic charges. We demonstrate that noncommutativity acts as a natural regulator, ensuring a finite total electromagnetic energy and thereby resolving the classical self-energy divergence. Furthermore, some of these solutions exhibit a non-perturbative dependence on the noncommutativity parameter and allow for the generation of an arbitrary magnetic flux. We also present a noncommutative generalization of Gauss's law, providing a robust framework for the physical interpretation of these exact solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_11736 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Poisson Gauge Theories in Three Dimensions: Exact Solutions and Conservation Laws Sharapov, Alexey Shcherbatov, David High Energy Physics - Theory We investigate Maxwell-Chern-Simons theory on a three-dimensional noncommutative spacetime endowed with a constant spacelike Poisson structure. By exploiting the residual rotational symmetry, we construct exact classical solutions corresponding to pointlike electric and magnetic charges. We demonstrate that noncommutativity acts as a natural regulator, ensuring a finite total electromagnetic energy and thereby resolving the classical self-energy divergence. Furthermore, some of these solutions exhibit a non-perturbative dependence on the noncommutativity parameter and allow for the generation of an arbitrary magnetic flux. We also present a noncommutative generalization of Gauss's law, providing a robust framework for the physical interpretation of these exact solutions. |
| title | Poisson Gauge Theories in Three Dimensions: Exact Solutions and Conservation Laws |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2604.11736 |