New electromagnetic fields in six-dimensional special relativity

By operating on two vector potentials with the two del operators which are defined with respect to three space and three time co-ordinates, new electromagnetic fields are obtained. The three fields introduced are the usual 3-component magnetic field, a new 3-component field W and a 9-component field which replaces the 3-component electric field of the standard four-dimensional theory. Extended Maxwell equations linking the three fields are established, as are their six-dimensional wave equations. Equations of motion of a charged particle in these fields are found, and it is shown how the new field W can affect the time curvature and the spatial motion of the particle. It is shown that no better symmetry is achieved by adding magnetic-monopole source terms to the extended Maxwell equations. It is shown how the vector potential, which replaces the scalar potential of the standard theory, may be constructed in the special cases of the fields due to a single charge and a dipole and that, in the latter case, the field does not possess the spatial symmetry of the corresponding four-dimensional theory. (author)