Poisson electrodynamics on $κ$-Minkowski space-time

Summary

The paper discusses Poisson electrodynamics on κ-Minkowski space-time, a semi-classical limit of U(1) non-commutative gauge theory. The authors study the interaction of a point-like charged particle with the Poisson gauge field, finding the deformed Lorentz force and possible effects of emergent gravity due to non-commutativity.

Highlights

• Poisson electrodynamics is a semi-classical limit of U(1) non-commutative gauge theory.
• The authors study the interaction of a point-like charged particle with the Poisson gauge field.
• The deformed Lorentz force is derived, showing possible effects of emergent gravity due to non-commutativity.
• The κ-Minkowski space-time is used to construct the equations of electrodynamics.
• The solutions for the potential and electric field of a point-like charge are obtained.
• The authors find that the electric field is finite at the origin, unlike in conventional Coulomb electrostatics.
• The non-commutativity parameter κ acts as a natural regulator for the electric field.

Key Insights

• The Poisson gauge transformations are defined, and the closure of the algebra is verified, ensuring consistency with the semi-classical limit.
• The symplectic realization is used to construct the gauge-invariant action, which is essential for deriving the deformed Lorentz force.
• The authors use the κ-Minkowski structure to study the interaction of a charged particle with the Poisson gauge field, leading to the derivation of the deformed Lorentz force.
• The effective potential is plotted as a function of radial distance, showing two return points for a negative energy in the case of α = -1/2.
• The orbital equation is derived, and numerical solutions are obtained, showing that the particle's trajectory is not closed due to the non-commutative nature of the space-time.
• The authors discuss the possibility of emergent gravity due to non-commutativity, which could be explored in future work.
• The results obtained in this paper demonstrate the potential of Poisson electrodynamics to describe the behavior of charged particles in non-commutative space-time.

Mindmap

Citation

Abla, O., & Neves, M. J. (2024). Poisson electrodynamics on $κ$-Minkowski space-time (Version 1). arXiv. https://doi.org/10.48550/ARXIV.2412.17202