Algebraic Aspects of Interactions of Massive Spinning Particles in Three Dimensions

TL;DR

This paper explores the algebraic structure of massive spinning particles in 2+1 dimensions, revealing that consistent quantization requires a critical gyromagnetic ratio of g=2 and proposing a perturbative quantization method in background fields.

Contribution

It introduces a general class of spinning particle models in three dimensions and analyzes their gauge algebra and constraints, identifying the critical gyromagnetic ratio for consistency.

Findings

Consistency requires gyromagnetic ratio g=2.

A perturbative quantization procedure is proposed.

The gauge algebra remains unbroken in specific models.

Abstract

The most general 2+1 dimensional spinning particle model is considered. The action functional may involve all the possible first order Poincare invariants of world lines, and the particular class of actions is specified thus the corresponding gauge algebra to be unbroken by inhomogeneous external fields. Nevertheless, the consistency problem reveals itself as a requirement of the global compatibility between first and second class constraints. These compatibility conditions, being unnoticed before in realistic second class theories, can be satisfied for a particle iff the gyromagnetic ratio takes the critical value g=2. The quantization procedure is suggested for a particle in the generic background field by making use of a Darboux co-ordinates, being found by a perturbative expansion in the field multipoles and the general procedure is described for constructing of the respective transformation in any order.