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arXiv · 2604.11736

Poisson Gauge Theories in Three Dimensions: Exact Solutions and Conservation Laws

Alexey Sharapov·David Shcherbatov
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Abstract

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.

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Alexey Sharapov, David Shcherbatov. 2026-04-13. Poisson Gauge Theories in Three Dimensions: Exact Solutions and Conservation Laws. https://arxiv.org/abs/2604.11736

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