To our present knowledge, there are four fundamental forces in Nature. We have already encountered gravity and electromagnetism, because they manifest themselves directly in the macroscopic world, and we have displayed the fundamental equations describing them. However, other known facts could not be explained by these two forces. For example, it was discovered that the nuclei of atoms were composed of smaller building blocks denoted neutrons and protons, the latter being positively charged. This raised the following question: if equal charges repel, how come these positively charged protons can all sit so peacefully together within the nucleus? Why doesn't the nucleus fly apart? The answer was simple: there is a force stronger than the electromagnetic force – properly referred to as the strong force – which keeps the nucleus together and which works on protons and neutrons in the same way. The theory describing this force is called Quantum Chromodynamics (QCD). During the 1970's it was discovered that the protons and neutrons themselves were composite particles too, each containing three so-called quarks. These quarks have never been observed as free isolated particles, because apparently they are permanently bound to each other and confined to the inside of particles called hadrons, like the proton and neutron. The quarks are subject to the strong force because they carry a kind of charge called ‘color’ (which has nothing to do with ordinary color), which keeps them tightly bound in these composites.

Quantum Chromodynamics describes the behavior of quarks and the strong force. This force is mediated by particles called gluons, because they ‘glue’ the quarks together in colorless composites called hadrons. There is a residual strong force between the hadrons, which for example binds neutrons and protons together in the nucleus. This is very similar to atomic physics, where the atoms are held together by the electromagnetic force, which is also responsible for the binding of atoms into molecules or other structures like crystals. Unlike quarks, electrons do not carry color and are therefore insensitive to the strong force. Hence they are not confined.

Quantum chromodynamics is completely specified by the first formula given. The second equation gives the definition of colorfields F in terms of the potentials A. The formulas are of remarkable beauty but deceiving simplicity.