Improved formalism for Abelian magnetic monopoles

Abstract

Euclidean lattice methods are used to derive an improved version of the Schwinger-Zwanziger Lagrangian for magnetic monopoles. The formalism involves a nondynamical string variable ${x}_{\ensuremath{\mu}}(\ensuremath{\sigma},\ensuremath{\tau})$. When the monopoles are coupled to a charged scalar field, ${x}_{\ensuremath{\mu}}$ can be utilized to absorb the dynamics of discontinuities in the angular part of the scalar field. In the Higgs phase where such discontinuities have finite action, ${x}_{\ensuremath{\mu}}$ becomes a dynamical variable and the Lagrangian becomes manifestly covariant. We derive the heuristic string-monopole equations of Nambu as the classical limit of the Higgs model in the London approximation.