Generalized Collective Coordinate Quantization of Solitons with Topological Terms

TL;DR

This paper introduces a generalized collective coordinate quantization method for solitons with topological terms, resolving issues in standard approaches and accurately reproducing baryon spectra in the Skyrme model.

Contribution

It proposes a novel quantization approach for solitons with topological terms, addressing zero mode classification and spectrum constraints.

Findings

Proper low energy effective theory constructed

Elimination of unwanted SU(3) multiplets

Reproduction of nucleon and delta baryon spectra

Abstract

We show that the $\theta+$ pentaquark does not exist in the Skyrme model. For the solitons of the theory with topological terms, the standard collective coordinate quantization does not construct the proper low energy effective theory. In the presence of topological terms, zero modes are classified into three groups: dynamical zero modes with constant velocity, cyclotron zero modes in a circular orbit, and static constraint zero modes. According to the mode expansion, the topological term contributes to the moduli metric of the dynamical zero modes. In addition, constraint zero modes do not have the kinetic term and produce constraints that strongly restrict the spectrum instead. In this paper, we propose a generalized collective coordinate quantization method and apply it to the SU(3) Skyrmion with the Wess- Zumino-Witten term. We find five constraints. These reproduce the results of [1], eliminating all the SU(3) multiplets except the nucleon octet and $\Delta$ baryon decuplet from the baryon spectrum.