Stringlike solution of the Higgs model with magnetic monopoles

We derive a static solution of the equations of motion following from a Higgs-type Lagrangian containing, in addition, static magnetic monopoles representing quarks. For this purpose, we use Zwanziger's approach to magnetic monopoles, and thus we are dealing with a local field theory for charged particles. We show that the solution has the form of a string of finite length for large coupling. We exhibit the dependence of the energy of the system ($E$) on interquark distance ($2\alpha$), $E\left(2a\right)=-\left(\frac{g^2}{8\pi a}\right)\exp \mathrm{}(-e|\mathrm{}{\Phi }_0\mathrm{}\left|2a\right)+C{\left|{\Phi }_0\right|}^{2}a$, which is the form found by Nambu in his discussion of this type of model as a scheme which offers a mechanism for quark confinement. We therefore confirm that Nambu's results can be reached in a field-theoretic formulation.