D=6 massive spinning particle

TL;DR

This paper introduces a six-dimensional massive spinning particle model with a specific configuration space, demonstrating its exact solvability and deriving wave equations consistent with 6D relativistic fields.

Contribution

It formulates a new 6D spinning particle model with a unique action based on Poincaré Casimir conservation, and shows its exact solvability and quantization.

Findings

Model is exactly solvable.

Quantization yields relativistic wave equations for 6D fields.

Action uniquely determined by Poincaré invariants.

Abstract

The massive spinning particle in six-dimensional Minkowski space is described as a mechanical system with the configuration space ${\ R}% ^{5,1}\times {\ CP}^3$. The action functional of the model is unambigiously determined by the requirement of identical (off-shell) conservation for the phase-space counterparts of three Casimir operators of Poincar\'e group. The model is shown to be exactly solvable. Canonical quantization of the model leads to the equations on wave functions which prove to be equivalent to the relativistic wave equations for the irreducible $6d$ fields.