On quantization of the SU(2) Skyrmions

TL;DR

This paper compares semiclassical and canonical quantization methods for SU(2) Skyrmions, showing they produce different results in the soliton's shape near the origin despite similar asymptotic behavior.

Contribution

It demonstrates that semiclassical and canonical quantization approaches are not equivalent and yield different profile functions for SU(2) Skyrmions.

Findings

The two quantization methods produce different shape profiles near the origin.

Both approaches lead to similar asymptotic behavior of the profile functions.

Canonical quantization introduces quantum mass corrections absent in semiclassical quantization.

Abstract

There are two known approaches for quantizing the SU(2) Skyrme model, the semiclassical and canonical quantization. The semiclassical approach does not take into account the non-commutativity of velocity of quantum coordinates and the stability of the semiclassical soliton is conveniently ensured by the symmetry breaking term. The canonical quantum approach leads to quantum mass correction that is not obtained in the semiclassical approach. In this letter we argue that these two approaches are not equivalent and lead to different results. We show that the resulting profile functions have the same asymptotic behaviour, however their shape in the region close to the origin is different.