The de Sitter Relativistic Top Theory

TL;DR

This paper explores the relativistic top theory within de Sitter and anti de Sitter groups, proposing a Kaluza-Klein based approach to derive equations of motion for spinning objects, extending previous formulations.

Contribution

It introduces a novel Kaluza-Klein method for deriving relativistic top equations from higher-dimensional geodesics, connecting group theory with spinning object dynamics.

Findings

Derived relativistic top equations from 4+N dimensional geodesics.

Compared and related to Fukuyama's spinning object formulation.

Extended the approach to 4+N+D dimensions.

Abstract

We discuss the relativistic top theory from the point of view of the de Sitter (or anti de Sitter) group. Our treatment rests on Hanson-Regge's spherical relativistic top lagrangian formulation. We propose an alternative method for studying spinning objects via Kaluza-Klein theory. In particular, we derive the relativistic top equations of motion starting with the geodesic equation for a point particle in 4+N dimensions. We compare our approach with the Fukuyama's formulation of spinning objects, which is also based on Kaluza-Klein theory. We also report a generalization of our approach to a 4+N+D dimensional theory.