The theory of the strong interaction of hadrons – quantum chromodynamics, or QCD – is in many ways the most perfect and non-trivial of the established microscopic theories of physics. It is, as far as is known, a self-consistent relativistic quantum field theory. But, unlike the case of the electromagnetic and weak interactions, many primary phenomena governed by QCD are not amenable to direct calculation by weak-coupling perturbation theory. Moreover, QCD has few parameters.

To understand these assertions, first recall the classification of known microscopic interactions into strong, electromagnetic, weak, and gravitational. Precisely because the strong interaction is strong, it is useful to study QCD by itself, the other interactions being perturbations.

QCD is a quantum field theory of the kind called a non-abelian gauge theory (or a Yang-Mills theory). It has two types of field: quark fields and the gluon field. Particles corresponding to the quark fields form the basic constituents of hadrons, like the proton, with the gluon field providing the binding between quarks. There appear to be no states for isolated quarks and gluons; these particles are always confined into hadrons. This contrasts with quantum electrodynamics (QED), where instead of quarks and gluons, we have electrons and photons, which do exist in isolated single-particle states.

One key feature of QCD is “asymptotic freedom”: the effective coupling of QCD goes to zero at zero distance. Thus short-distance processes yield to the highly developed methods of Feynman perturbation theory.