7 - Confinement

Summary

Introduction

A brief historical overview

While the prehistory of the question begins with the discovery of strong interactions (the nucleon model of atomic nuclei was developed in 1932), the origin of the confinement story may, perhaps, be referred to the year of 1961. By the early 1960s quite a number of strongly interacting particles had been discovered (π, K; K; N, ∧, Σ, Ξ, Δ, Σ*, Ξ*), and the problem of finding some kind of systematic order in this zoo of “elementary building blocks” of matter became rather urgent. M. Gell-Mann and J. Neeman (see [338–340]) proposed a classification of these particles by the group SU(3) (in modern terminology, the flavor group SU(3)_f). The classification scheme was known as the “eightfold way”: mesons (π, K, η) and barions (N, ∧, Σ, Ξ) were organized into octet representations of SU(3)_f. However, the observed particles realized only particular representations of SU(3)_f (the octet and decuplet (Δ, Σ*, Ξ*, Ω^-) ones); the role of other representations was not clear. As is well known, all representations of the group SU(3) can be constructed from the two simplest triplets, ξ and ξ*, being the so-called fundamental representation and its dual [218]. M. Gell-Mann and G. Zweig (see [341, 342]) assumed that all strongly interacting particles (hadrons) are built of elementary objects realizing the fundamental representation of SU(3)_f (“quarks” [341] or “aces” [342]).