Batalin-Tyutin Quantisation of the $CP^{N-1}$ model

TL;DR

This paper applies Batalin-Tyutin quantisation to the $CP^{N-1}$ model, converting second class constraints into first class to facilitate quantisation and avoid operator ordering ambiguities.

Contribution

It provides a detailed implementation of Batalin-Tyutin formalism for the $CP^{N-1}$ model, including explicit calculations of constraints, Hamiltonian, and BRST charge.

Findings

First class constraints and BRST charge explicitly derived.

Partition function evaluated in the unitary gauge.

Operator ordering ambiguities avoided in this formalism.

Abstract

The $CP^{N-1}$ model is quantised in the generalised canonical formalism of Batalin and Tyutin by converting the original second class system into first class. Operator ordering ambiguities present in the conventional quantisation scheme of Dirac are thereby avoided. The first class constraints, the involutive Hamiltonian and the BRST charge are explicitly computed. The partition function is defined and evaluated in the unitary gauge.