Electrodynamics on $\kappa$-Minkowski space-time

TL;DR

This paper derives electrodynamics equations on kappa-Minkowski space-time, revealing how non-commutativity influences electromagnetic phenomena, including charge scaling and mass dependence, by extending classical principles to a quantum-deformed space-time.

Contribution

It introduces a derivation of Lorentz and Maxwell's equations on kappa-Minkowski space-time using minimal coupling, establishing their equivalence with Feynman's approach and analyzing non-commutative effects.

Findings

Electric charge is scaled in the static limit due to kappa deformation

Electrodynamics laws depend on the mass of charged particles

Motion can be interpreted as in a background gravitational field

Abstract

In this paper, we derive Lorentz force and Maxwell's equations on kappa-Minkowski space-time up to the first order in the deformation parameter. This is done by elevating the principle of minimal coupling to non-commutative space-time. We also show the equivalence of minimal coupling prescription and Feynman's approach. It is shown that the motion in kappa space-time can be interpreted as motion in a background gravitational field, which is induced by this non-commutativity. In the static limit, the effect of kappa deformation is to scale the electric charge. We also show that the laws of electrodynamics depend on the mass of the charged particle, in kappa space-time.