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We study the issue of description of spinning particle dynamics by means ofrecently proposed world sheet concept. A model of irreducible spinning particlein the $3d$ Minkowski space with two gauge symmetries is considered. Theclassical trajectories of free particle lie on a circular cylinder with atime-like axis. The direction of cylinder axis is determined by the particlemomentum, and its position in space-time depends on the value of total angularmomentum. The radius of cylinder is determined by the representation. The modeladmits inclusion of consistent interactions with a general (not necessarilyuniform) electromagnetic field. The classical trajectories of the particle lieon the cylindrical hypersurface in space time, whose position is determined bythe initial values of the momentum and total angular momentum. All the worldpaths that lie on one and the same representative in the set of hypersufacesare connected by gauge transformations. The general construction is illustratedby the example of unform electric field. In this case, the particle paths areshown to be general pseudotoroidal lines.

On the world sheet of anyon in the external electromagnetic field