  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.
