Quantisation of $O(N)$ invariant nonlinear sigma model in the Batalin-Tyutin formalism

TL;DR

This paper applies the Batalin-Tyutin formalism to quantise the $O(N)$ nonlinear sigma model, overcoming operator ordering ambiguities present in traditional methods, and explicitly constructs the BRST charge and partition function.

Contribution

It demonstrates a nontrivial application of the BT method to a complex nonlinear sigma model, providing explicit quantisation and gauge fixing procedures.

Findings

Explicit BRST charge and Hamiltonian derived

Partition function constructed in different gauges

Overcomes operator ordering ambiguities in quantisation

Abstract

We quantise the $O(N)$ nonlinear sigma model using the Batalin Tyutin (BT) approach of converting a second class system into first class. It is a {\it nontrivial} application of the BT method since the quantisation of this model by the conventional Dirac procedure suffers from operator ordering ambiguities. The first class constraints, the BRST Hamiltonian and the BRST charge are explicitly computed. The partition function is constructed and evaluated in the unitary gauge and a multiplier (ghost) dependent gauge.