Solutions with both magnetic and electric charges in a (4+N)-dimensional geometric field theory

Abstract

We study classical solutions with both magnetic and electric charges in a ($4+N$)-dimensional geometric field theory. Then we choose the group SO(3,1) for the internal symmetry and try to find the solutions under the ansatz that they are invariant with respect to the diagonal subgroup of $\mathrm{SO}{(3,1)}_{M} \ensuremath{\bigotimes} \mathrm{SO}{(3,1)}_{I}$ in order to get relativistically covariant solutions, where $\mathrm{SO}{(3,1)}_{M}$ and $\mathrm{SO}{(3,1)}_{I}$ represent SO(3,1) for rotations of the Minkowski space and for the internal symmetry, respectively. Thus we obtain solutions having a covariant expression for the electromagnetic field associated with magnetic and electric charges moving with constant velocity. Particles with both magnetic and electric charges are usually referred to as dyons. Hence our solutions give a specific realization of dyons in a uniform motion. As a result of the incorporation of the internal symmetry $\mathrm{SO}{(3,1)}_{I}$, furthermore, it is found that they have a new pole in addition to the magnetic and electric charges. The gauge fields associated with this pole contribute negative energy. Then there exists a relation among the three kinds of charges, which gives a lower bound to the absolute value of the electric charge. Finally, we discuss the stability of our solutions.