Hamiltonian formulation of monopole theories with strings

Abstract

We consider the Hamiltonian formulation of the theory resulting from Direc's monopole action supplemented by a mass term for the gauge field. The original (zero-mass gauge field) theory is also discussed and its Hamiltonian is shown to be essentially the same as that of the two-potential formalism. In this case, the coordinates of the string are absorbed into what turn out to be the physically meaningful variables for the particles and the field. In the massive case, the string does play a significant role and gives rise to a static linear potential and a Yukawa potential between the monopoles. Such a potential has also been found by Nambu and others and may lead to an acceptable model for interactions of quarks.