The Batalin-Tyutin Formalism on the Collective Coordinates Quantisation of the SU(2) Skyrme Model

TL;DR

This paper applies the Batalin-Tyutin formalism to the SU(2) Skyrme model's collective coordinate quantisation, introducing an extended phase space that potentially enhances the model's phenomenological predictions.

Contribution

It demonstrates how the Batalin-Tyutin constraint formalism can be used to convert second class constraints into first class constraints in the Skyrme model's quantisation.

Findings

Derived the first class constraints and Hamiltonian in extended phase space.

Constructed and evaluated the vacuum functional in different gauges.

Identified an additional term in the quantum Hamiltonian that may improve phenomenology.

Abstract

We apply The Batalin-Tyutin constraint formalism of converting a second class system into a first class system for the rotational quantisation of the SU(2) Skyrme model. We obtain the first class constraint and the Hamiltonian in the extended phase space. The vacuum functional is constructed and evaluated in the unitary gauge and a multiplier dependent gauge. Finally, we discuss the spectrum of the extended theory. The use of the BT formalism on the collective coordinates quantisation of the SU(2) Skyrme model leads an additional term in the usual quantum Hamiltonian that can improve the phenomenology predicted by the Skyrme model.