Quantization of spherically symmetric solution of SU(3) Yang-Mills theory

TL;DR

This paper applies a quantization method to classical SU(3) Yang-Mills solutions, reducing unphysical behavior at large distances while preserving short-distance features, potentially aiding in understanding quantum corrections.

Contribution

It introduces a quantization approach inspired by Heisenberg to modify classical solutions of SU(3) Yang-Mills fields, addressing issues of infinite energy.

Findings

Quantization softens unphysical large-distance behavior

Short-distance properties of solutions are preserved

Method may serve as a general tool for quantum corrections

Abstract

A recent investigation of the SU(3) Yang-Mills field equations found several classical solutions which exhibited a type of confinement due to gauge fields which increased without bound as $r \to \infty$. This increase of the gauge fields gave these solutions an infinite field energy, raising questions about their physical significance. In this paper we apply some ideas of Heisenberg about the quantization of strongly interacting, non-linear fields to this classical solution and find that at large $r$ this quantization procedure softens the unphysical behaviour of the classical solution, while the interesting short distance behaviour is still maintained. This quantization procedure may provide a general method for approximating the quantum corrections to certain classical field configurations.