Exact solutions to noncommutative 3D Maxwell-Chern-Simons theory yield finite energy for point charges, permit arbitrary magnetic flux through non-perturbative dependence on the deformation parameter, and include a generalized Gauss law.
The electromagnetic field in Poisson gauge the- ory: the groupoidal approach
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Conservation laws including energy-momentum tensor and charge are derived for Lie-Poisson field theories; the non-relativistic κ-Minkowski Dirac equation introduces an orbital Zeeman term whose energy shift depends only on the κ parameter.
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Poisson Gauge Theories in Three Dimensions: Exact Solutions and Conservation Laws
Exact solutions to noncommutative 3D Maxwell-Chern-Simons theory yield finite energy for point charges, permit arbitrary magnetic flux through non-perturbative dependence on the deformation parameter, and include a generalized Gauss law.
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Conservation laws in Lie-Poisson classical field theories
Conservation laws including energy-momentum tensor and charge are derived for Lie-Poisson field theories; the non-relativistic κ-Minkowski Dirac equation introduces an orbital Zeeman term whose energy shift depends only on the κ parameter.