SU(3) is a mathematical symmetry group called the special unitary group of order 3. It is related to quantum chromodynamics (QCD), which is a quantum field theory describing the strong nuclear force that binds quarks together to form particles such as protons and neutrons.
In the context of particle physics, the fundamental building blocks of matter are elementary particles known as quarks. Quarks come in different flavors, namely up (u), down (d), strange (s), charm (c), top (t), and bottom (b). Quantum chromodynamics is the theory that governs the strong interactions between these quarks.
QCD is a gauge theory based on the principles of quantum mechanics and special relativity, and it possesses a local symmetry called SU(3) gauge symmetry. The SU(3) symmetry arises from the fact that there are three different types of quarks (up, down, and strange), each with its corresponding color charge (red, green, and blue).
The SU(3) symmetry in QCD allows for the exchange of particles called gluons, which carry the color charge and mediate the strong force. The strong force is responsible for holding quarks together within a proton or neutron and for binding protons and neutrons within atomic nuclei.
The mathematics of SU(3) plays a crucial role in formulating the equations and describing the interactions of QCD. The interactions between quarks and gluons are expressed through the SU(3) gauge symmetry and the associated mathematical formalism. This symmetry provides a framework to understand and calculate various properties of the strong nuclear force, such as the behavior of quarks within hadrons, the creation and annihilation of quark-antiquark pairs, and the confinement of quarks.
In summary, SU(3) is the symmetry group associated with quantum chromodynamics (QCD), the theory describing the strong nuclear force. The SU(3) symmetry plays a central role in formulating the equations and understanding the interactions of QCD, allowing for a mathematical description of the behavior of quarks and gluons within the strong force.