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

## TL;DR

This paper introduces a geometric model for a massive spinning particle in four-dimensional Minkowski space, where particle trajectories are constrained to cylinders defined by momentum and angular momentum, emphasizing a gauge-invariant, non-Lagrangian approach.

## Contribution

The paper presents a novel geometrical model of a massive spinning particle that does not require additional spin variables and derives implicit equations of motion based on path curvature and helices.

## Key findings

- Particle paths lie on cylinders determined by momentum and angular momentum.
- Equations of motion are implicit, gauge-invariant, and non-Lagrangian.
- Explicit equations are derived for small curvature and helical trajectories.

## Abstract

We propose the model of massive spinning particle traveling in four-dimensional Minkowski space. The equations of motion of the particle follow from the fact that all the classical paths of the particle lie on a cylinder whose position in Minkowski space is determined by the particle's linear momentum and total angular momentum. 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 found 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 geometrical character, with no additional variables in the space of spin states being introduced.