Geometrical model of massive spinning particle in four-dimensional Minkowski space

Abstract

Abstract We propose the model of a massive spinning particle traveling in four-dimensional Minkowski space. The equations of motion of the particle are obtained from the requirement that its classical paths lie on a cylinder with the time-like axis in Minkowski space. All the paths on one and the same cylinder are gauge equivalent. The equations of motion are found in implicit form for general time-like paths, and they are non-Lagrangian. The explicit equations of motion are derived for trajectories with small curvature and helices. The momentum and total angular momentum are expressed in terms of characteristics of the path in all the cases. The constructed model of the spinning particle has a geometrical character, with no additional variables in the space of spin states being introduced.