Quantum Chromodynamics Theory
Quantum Chromodynamics, or QCD, is the theory describing the strong interactions between quarks and gluons. These interactions are responsible for binding quarks together into nucleons and mesons, and also for binding the nucleons together inside atomic nuclei.
QCD is quite similar in many respects to Quantum electrodynamics (QED). Instead of the positive and negative electric charges found in QED, QCD has three positive charges called colors. The names given to the colors vary, but a common scheme is red, green and blue. The negative charges usually are called anti-red, anti-green, and anti-blue. QED has one photon, a massless force-carrier particle, compared to QCD's eight massless force-carrier particles, the gluons.
The largest difference between QCD and QED lies in the group structure of the two theories. QED has a symmetry under an Abelian group called U(1), similar to the group of two-dimensional rotations. In an Abelian group, symmetry transformations can be performed in any order with the same effect (they commute). QCD has a symmetry under a more general non-Abelian group called SU(3), where the order of the symmetry transformations matters. The upshot of these mathematical notions is found when applying the renormalization theory. Forces described by Abelian theories become stronger at higher energies, while the forces described by non-Abelian theories become weaker at higher energies. The converse is also true; non-Abelian forces become stronger at lower energies, but Abelian forces become weaker at lower energies.
The strong force described by QCD is extremely strong at low energies, resulting in a property of quarks known as confinement. Quarks are confined in either nucleons or mesons at low energies. They cannot be pulled apart, explaining why lone quarks do not exist. At high energies accessible to particle accelerators, however, the QCD force is much weaker. This explains why scattering from nucleons can be described accurately by describing the quarks as free particles inside the nucleon.
Because of its strength at low energies, low energy calculations in QCD theory are very difficult. The usual procedure for accomplishing calculations in quantum field theory is called perturbation theory, but it requires that the force be weak. Difficult differential equations of QCD, therefore, must be solved explicitly using computer algorithms. One successful technique, lattice QCD, has been developed, where calculations are done on a discrete lattice, and at the end of the calculation, a limit of the answer is taken when the lattice spacing is zero. Because the calculations require much computing time and clever algorithms, development of lattice QCD has been very challenging. Although QCD is well verified, it remains to many physicists a frustrating theory because of the difficulty in calculating its low-energy effects.
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