Extended particles and magnetic charges

It is shown that in more than two space dimensions a field theory having no massless particles cannot have solutions of the field equations which are periodic in time, have finite energy, and are separated from the vacuum by an infinite potential barrier. In three space dimensions an infinite potential barrier can exist only between solutions with different magnetic charge. In any gauge theory in three space dimensions the magnetic charge is shown to have an intrinsic topological nature. The group $\mathrm{SU}\mathrm{}\left(n\right)\mathrm{}$ is analyzed in detail and shown to have $n-1\mathrm{}$ types of magnetic charges. The infinite nature of the potential barrier is shown to be relevant for the semiclassical approximation to the path-integral quantization.