Maxwell's equations and Lorentz force in doubly special relativity

TL;DR

This paper extends Maxwell's equations and Lorentz force to doubly special relativity using k-deformed phase space, revealing new effects like a gravitational-type Lorentz force dependent on electromagnetic fields.

Contribution

It derives an extended form of Maxwell's equations and Lorentz force in DSR incorporating k-deformation, highlighting new mass-dependent and gravitational-like effects.

Findings

Derived extended Maxwell's equations in DSR with k-deformation.

Identified a gravitational-type Lorentz force induced by phase space deformation.

Showed dependence of electrodynamics laws on particle mass in DSR.

Abstract

On the basis of all commutation relations of the k-deformed phase space incorporating the k-Minkowski space-time, we have derived in this paper an extended first approximation of both Maxwell's equations and Lorentz force in doubly (or deformed) special relativity (DSR). For this purpose, we have used our approach of the special relativistic version of Feynman's proof by which we have established the explicit formulations of electric and magnetic fields. As in Fock's nonlinear relativity (FNLR), the laws of electrodynamics depend on the particle mass which therefore constitutes a common point between the two extended forms of special relativity. As one consequence, the corresponding equation of motion contains two different types of contributions. In addition to the usual type, another one emerges as a consequence of the coexistence of mass and charge which are coupled with the k-deformation and electromagnetic field. This new effect completely induced by the k-deformed phase space is interpreted as the gravitational-type Lorentz force. Unlike FNLR, the corrective terms all depend on the electromagnetic field in DSR.