Spinning particles, coadjoint orbits and Hamiltonian formalism

TL;DR

This paper provides a detailed Hamiltonian analysis of relativistic spinning particles using coadjoint orbits, including classification of constraints, symmetry analysis, and canonical quantization leading to Poincare group representations.

Contribution

It introduces a Hamiltonian formalism for spinning particles based on coadjoint orbits, with explicit factorization of Lorentz transformations and a complete constraint classification.

Findings

Explicit Hamiltonian dynamics for spinning particles derived

Constraints classified into first and second class with symmetry analysis

Canonical quantization yields irreducible Poincare group representations

Abstract

The extensive analysis of the dynamics of relativistic spinning particles is presented. Using the coadjoint orbits method the Hamiltonian dynamics is explicitly described. The main technical tool is the factorization of general Lorentz transformation into pure boost and rotation. The equivalent constrained dynamics on Poincare group (viewed as configuration space) is derived and complete classification of constraints is performed. It is shown that the first class constraints generate local symmetry corresponding to the stability subgroup of some point on coadjoint orbit. The Dirac brackets for second class constraints are computed. Finally, canonical quantization is performed leading to infinitesimal form of irreducible representations of Poincare group.