Electrodynamics in flat spacetime of six dimensions

Abstract

This paper considers the dynamics of a classical charge in flat spacetime of six dimensions. The mass-shell relation of a free charge allows nonlinear oscillations. Having analyzed the problem of eigenvalues and eigenvectors of the Faraday tensor, we established the algebraic structure of the electromagnetic field in 6D. The classification scheme based on three field invariants is thoroughly elaborated. Using the basic algebraic properties of the electromagnetic field tensor, we examine the motion of a charge in a constant electromagnetic field. Its world line is a combination of hyperbolic and circular orbits that 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. As it turns out, spins of elementary particles themselves are manifestations of extra dimensions.