Extended objects in a gauge theory

The covariant description of extended objects (Soliton) in the quantum field theory of two dimensions using relativistically covariant collective coordinates was presented previously. This method can be applied to higher dimensions and gauge theories. In this paper, the Abelian Higgs model in three dimensions is discussed. The Lagrangian density with primary and secondary constraints is introduced. Some choice of the gauge conditions is made, and six numbers of coordinates are introduced. The variables are transformed by Poincare transformation. First, the constraints of the gauge field is solved by adding a secondary constraint. The other six constraints associated with collective coordinates are consistent with each other with respect to the Dirac bracket. The gauge conditions are fixed so that the new frame means a body fixed one. The calculation of the mass of an extended object can be done. Rotational collective spectra appear in a mass term from the integration of these zero-energy modes. Finally, a scalar form factor of the extended object in three dimensions is presented. (Kato, T.)