Electrodynamics in flat spacetime of six dimensions

TL;DR

This paper explores the dynamics of a classical charge in six-dimensional flat spacetime, analyzing electromagnetic field algebraic structures, charge motion, and implications for particle spins within a braneworld context.

Contribution

It provides a detailed algebraic classification of electromagnetic fields in 6D and examines charge trajectories, linking extra dimensions to particle spin phenomena.

Findings

Charge mass shell exhibits nonlinear oscillations.

Electromagnetic field classification based on three invariants.

Charge trajectories combine hyperbolic and circular orbits.

Abstract

We consider the dynamics of a classical charge in flat spacetime of six dimensions. The mass shell relation of a free charge admits nonlinear oscillations. Having analyzed the problem of on eigenvalues and eigenvectors of Faraday tensor, we establish the algebraic structure of electromagnetic field in 6D. We elaborate the classification scheme based on three field's invariants. Using the basic algebraic properties of the electromagnetic field tensor we analyze the motion of a charge in constant electromagnetic field. Its world line is a combination of hyperbolic and circular orbits which lie in three mutually orthogonal sheets of two dimensions. Within the braneworld scenario, we project the theory on the de Sitter space of four dimensions. Actually, as it turns out, spins of elementary particles themselves are manifestations of extra dimensions.