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

TL;DR

This paper investigates how point-like charged particles interact with Poisson gauge fields on $kappa$-Minkowski space-time, revealing potential emergent gravity effects due to non-commutative geometry.

Contribution

It constructs a gauge-invariant action for particles interacting with Poisson electrodynamics on $kappa$-Minkowski space-time and derives the deformed Lorentz force equations.

Findings

Derived second-order deformed Lorentz force equations

Identified potential emergent gravity effects from non-commutativity

Analyzed particle trajectories in $kappa$-Minkowski space-time

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.