World sheets of spinning particles
D.S. Kaparulin, S.L. Lyakhovich

TL;DR
This paper explores the geometric structure of classical spinning particles, revealing that their world lines form cylindrical or toroidal world sheets in Minkowski space, and derives equations of motion with gauge symmetries for these particles.
Contribution
It introduces a geometric description of spinning particles' world sheets as cylinders or tori and derives their classical equations of motion with gauge symmetries, connecting to known models.
Findings
World sheets are cylinders in 3D and 4D, tori in higher dimensions.
Derived a fourth-order differential equation for particle paths with gauge symmetries.
Established an equivalent second-order formulation with auxiliary variables.
Abstract
The classical spinning particles are considered such that quantization of classical model leads to an irreducible massive representation of the Poincar\'e group. The class of gauge equivalent classical particle world lines is shown to form a -dimensional world sheet in -dimensional Minkowski space, irrespectively to any specifics of classical model. For massive spinning particles in , the world sheets are shown to be cylinders. The radius of cylinder is fixed by representation. In higher dimensions, particle's world sheet turn out to be a toroidal cylinder , . Proceeding from the fact that the world lines of irreducible classical spinning particles are cylindrical curves, while all the lines are gauge equivalent on the same world sheet, we suggest a method to deduce the classical equations of motion for particles and also…
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