Quantized Skyrmion Fields in 2+1 Dimensions

TL;DR

This paper develops a fully quantized field theory for skyrmions in 2+1 dimensions, enabling calculation of correlation functions and analysis of quantum effects on skyrmion properties, including mass and statistics.

Contribution

It introduces a novel quantization method for skyrmion fields in 2+1D and computes quantum corrections to skyrmion mass and statistics.

Findings

Quantum skyrmion mass is reduced compared to classical mass.

Correlation functions are explicitly calculated in various interaction scenarios.

Quantum effects influence skyrmion properties, confirming semiclassical predictions.

Abstract

A fully quantized field theory is developped for the skyrmion topological excitations of the O(3) symmetric CP$^1$-Nonlinear Sigma Model in 2+1D. The method allows for the obtainment of arbitrary correlation functions of quantum skyrmion fields. The two-point function is evaluated in three different situations: a) the pure theory; b) the case when it is coupled to fermions which are otherwise non-interacting and c) the case when an electromagnetic interaction among the fermions is introduced. The quantum skyrmion mass is explicitly obtained in each case from the large distance behavior of the two-point function and the skyrmion statistics is inferred from an analysis of the phase of this function. The ratio between the quantum and classical skyrmion masses is obtained, confirming the tendency, observed in semiclassical calculations, that quantum effects will decrease the skyrmion mass. A brief discussion of asymptotic skyrmion states, based on the short distance behavior of the two-point function, is also presented.