arXiv subjects

David Shcherbatov

Publications and source records attributed to David Shcherbatov.

3 recordsLinked to original sources

arXiv2026

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

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.

hep-th↗

arXiv2024

Electromagnetic Interactions of Massive Higher-Spin Fields in 3D via Chiral Theory

We address the issue of electromagnetic interaction for massive higher-spin fields in $3d$ Minkowski space. We show that consistent field equations can be obtained through the dimensional reduction of the higher-spin extension of self-dual Yang-Mills theory, which itself is a truncation of chiral higher-spin gravity in four dimensions. The resulting electromagnetic field satisfies the Bogomolny equation, and the interaction is non-minimal with the gyromagnetic ratio given by $g=1/s$, where $s$ is the spin. As a by-product, we obtain a new Lagrangian for free massive higher-spin fields in $3d$.

hep-th↗

arXiv2023

On auxiliary fields and Lagrangians for relativistic wave equations

We address the problem of the existence of a Lagrangian for a given system of linear PDEs with constant coefficients. As a subtask, this involves bringing the system into a pre-Lagrangian form, wherein the number of equations matches the number of unknowns. We introduce a class of overdetermined systems, called co-flat, and show that they always admit a pre-Lagrangian form, which can be explicitly constructed using auxiliary variables. Moreover, we argue that such systems enjoy pre-Lagrangian formulations without auxiliary variables at all. As an application of our method, we construct new pre-Lagrangian and Lagrangian formulations for free massive fields of arbitrary integer spin. In contrast to the well-known models of Singh and Hagen, our Lagrangians involve much fewer auxiliary fields.

hep-th↗