SU(N) groups

SU(N) groups are mathematical structures used in physics to describe symmetries, especially in quantum mechanics and particle physics. They consist of special unitary matrices—complex square matrices with determinant one—that preserve certain properties when combined. These groups capture how particles and forces behave under symmetry transformations, like rotations or phase changes, which leave physical laws unchanged. The parameter N indicates the dimension of the matrices; for example, SU(2) relates to spin, and SU(3) to color charge in quarks. Overall, SU(N) groups help us understand fundamental particles' behavior via symmetrical mathematical frameworks.