The non-abelian BFFT formalism for the collective coordinates quantization of the SU(2) Skyrme model

TL;DR

This paper applies the non-abelian BFFT formalism to convert second class constraints into first class constraints in the SU(2) Skyrme model, simplifying the algebra and confirming consistent quantization.

Contribution

It introduces a non-abelian BFFT approach to the Skyrme model, providing simplified Hamiltonians and demonstrating the method's richness over the abelian version.

Findings

Derived simplified first class Hamiltonians

Reproduced original Skyrmion Lagrangian when extended variables are zero

Confirmed consistent spectrum through Dirac quantization

Abstract

The collective coordinates expansion of the Skyrme soliton particle model gives rise to the second class constraints. We use the non-abelian BFFT formalism to convert this system into the one with only first class constraints. Choosing two different structure functions of the non-abelian algebra, we obtain simplified algebraic expressions for the first class non-abelian Hamiltonians. This result shows that the non-abelian BFFT method is, in many aspects, richer than the abelian BFFT formalism. For both of the first class Hamiltonians, we derive the Lagrangians which lead to the new theory. When one puts the extended phase space variables equal to zero, the original Skyrmion Lagrangian is reproduced. The method of the Dirac first class constraints is employed to quantize these two systems. We achieve the same spectrum, a result which confirms the consistency of the non-abelian BFFT formalism.