Batalin-Tyutin Quantisation of the Spinning Particle Model

TL;DR

This paper applies the Batalin-Tyutin quantisation method to the spinning particle model for anyons, introducing extra degrees of freedom to convert all constraints into first class, simplifying quantisation and revealing non-commutative space-time effects.

Contribution

It demonstrates the application of Batalin-Tyutin quantisation to the spinning particle model, recovering known results and highlighting the role of extended phase space variables.

Findings

Recovery of gyromagnetic ratio g=2 for anyons

Explicit computation of Batalin-Tyutin variable contributions

Identification of non-commutative space-time effects

Abstract

The Spinning Particle Model for anyon is analysed in the Batalin-Tyutin scheme of quantisation in extended phase space. Here additional degrees of freedom are introduced in the phase space such that all the constraints in the theory are rendered First Class that is commuting in the sense of Poisson Brackets. Thus the theory can be studied without introducing the Dirac Brackets which appear in the presence of non-commuting or Second Class constraints. In the present case the Dirac Brackets make the configuration space of the anyon non-canonical and also being dynamical variable dependent, poses problems for the quantisation programme. We show that previously obtained results, (e.g. gyromagnetic ratio of anyon being 2), are recovered in the Batalin-Tyutin variable independent sector in the extended space. The Batalin-Tyutin variable contributions are significant and are computable in a straightforward manner. The latter can beunderstood as manifestations of the non-commutative space-time in the enlarged phase space.