Dirac quantization and baryon intrinsic frequencies in hypersphere soliton model

TL;DR

This paper quantizes a hypersphere soliton model to predict baryon properties, finding good agreement with experimental data and revealing intrinsic pulsation frequencies related to baryon masses.

Contribution

It introduces a first class Hamiltonian quantization of the hypersphere soliton, improving predictions of baryon masses and intrinsic frequencies compared to previous methods.

Findings

Predicted axial coupling constant matches experimental value.

Improved delta baryon mass prediction with Weyl ordering correction.

Intrinsic frequencies of nucleon and delta baryon are proportional, with _{}= extstyle 2 \u03c9_N.

Abstract

Quantizing a soliton on a hypersphere, we obtain the first class Hamiltonian, and evaluate the baryon physical quantities which are in good agreement with the corresponding experimental data. In particular, we find that the predicted value for axial coupling constant is comparable to its experimental value. The prediction for delta baryon mass possessing the Weyl ordering correction obtained in the first class Dirac quantization is improved comparing with that in the second class canonical quantization performed on the hypersphere. Making use of the same input parameters associated with the baryon masses, we also investigate the hypersphere soliton and standard Skyrmion models to compare the corresponding predictions for the physical quantities effectively. Next, we evaluate the intrinsic frequencies of the pulsating baryons. We thus find that the intrinsic pulsating frequency of more massive particle is greater than that of the less massive one. We explicitly evaluate the intrinsic frequencies $\omega_{N}=0.87\times 10^{23}~{\rm sec}^{-1}$ and $\omega_{\Delta}=1.74\times 10^{23}~{\rm sec}^{-1}$ of the nucleon and delta baryon, respectively, to yield the identity $\omega_{\Delta}=2\omega_{N}$.