Exact solutions in the Yang-Mills-Wong theory

TL;DR

This paper systematically derives exact retarded solutions to classical SU(N) Yang-Mills equations with multiple colored point sources, proposing a toy model for quark binding that aligns with known phenomenology and explores the stability of quark clusters.

Contribution

It introduces a new method for finding exact solutions to Yang-Mills equations with sources and applies it to model quark interactions and stability of multiquark clusters.

Findings

Exact solutions for SU(N) Yang-Mills equations with multiple sources

A toy model explaining quark binding without confinement

Analysis of cluster stability based on gauge group considerations

Abstract

This paper discusses in a systematical way exact retarded solutions to the classical SU(N) Yang-Mills equations with the source composed of several colored point particles. A new method of finding such solutions is reviewed. Relying on features of the solutions, a toy model of quark binding is suggested. According to this model, quarks forming a hadron are influenced by no confining force in spite of the presence of a linearly rising term of the potential. The large-N dynamics of quarks conforms well with Witten's phenomenology. On the semiclassical level, hadrons are color neutral in the Gauss law sense. Nevertheless, a specific multiplet structure is observable in the form of the Regge sequences related to infinite-dimensional unitary representations of SL(4,R) which is shown to be the color gauge group of the background field generated by any hadron. The simultaneous consideration of SU(N), SO(N), and Sp(N) as gauge groups offers a plausible explanation of the fact that clusters containing two or three quarks are more stable than multiquark clusters.