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arXiv · 2412.17202

Poisson electrodynamics on $\kappa$-Minkowski space-time

O. Abla·M. J. Neves
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Abstract

Poisson electrodynamics is the semi-classical limit of $U(1)$ non-commutative gauge theory. It has been studied so far as a theoretical model, where an external field would be the source of the non-commutative effects in space-time. Being the Standard Model of fundamental interactions a local theory, the prediction of observables within it would be drastically altered by such effects. The natural question that arises is: how do particles interact with this field ? In this work, we will answer this question using point-like charged particles interacting with the Poisson gauge field, investigating how their trajectories are affected using the $\kappa$-Minkowski structure. The interaction arises from the construction of a gauge-invariant action. Using the field solutions, we find the second-order equation for the deformed Lorentz force, indicating possible effects of an emergent gravity due to non-commutativity.

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O. Abla, M. J. Neves. 2024-12-23. Poisson electrodynamics on $\kappa$-Minkowski space-time. https://doi.org/10.1016/j.physletb.2025.139385

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