Extended objects created by Goldstone bosons

Extended objects which appear in relativistic quantum field theory with spontaneous breakdown of symmetries are studied. The extended objects are created through the condensation of the Goldstone bosons. The condensation is mathematically expressed by the boson transformation. The topological singularities are defined by means of the noncommutability condition among the derivatives acting on the boson transformation parameters which are functions of space and time coordinates. A systematic method for constructing the extended objects with topological singularities is presented. It is found that the extended objects can carry a full variety of topological singularities. Only some of the topological constants associated with these topological singularities are quantized. Though the choice of original symmetry does not restrict the choice of topological singularities, it does restrict the choice of quantized topological constants (topological quantum numbers). Special effort is devoted to the construction of the extended objects which are confined in a finite domain of the three-dimensional space. In particular, a spherical surface singularity (a ''bag'') is obtained explicitly. Furthermore, it is shown that instantaneous singularities and transient singularities are also acceptable to our scheme