SU3c

SU(3)_c, or SU(3) color, is the color gauge group of quantum chromodynamics (QCD). It is the special unitary group of degree 3: the set of 3×3 complex matrices U with U†U = I and det U = 1. As a compact Lie group, its dimension is eight, with generators T^a (a = 1,…,8) satisfying [T^a, T^b] = i f^{abc} T^c. The center of SU(3) is Z3.

In the Standard Model, SU(3)_c is a local gauge symmetry governing the strong interaction. Quarks transform in the fundamental representation 3 and carry color charge; antiquarks transform in 3̄. Gluons transform in the adjoint representation 8 and act as the gauge bosons of the symmetry. The QCD Lagrangian contains the gauge field strength F^a_{μν} and gluon fields A^a_μ, with a gauge coupling g_s; non-Abelian self-interactions arise from the structure constants f^{abc}.

Key properties include asymptotic freedom, meaning the coupling decreases at high energies, and confinement at low energies, preventing isolation of color charges. The theory is renormalizable and its coupling runs with energy according to β function: β(g_s) = -β0 g_s^3/(16π^2) + ..., with β0 = 11 − 2n_f/3 for SU(3) with n_f quark flavors. Representations of color determine particle content: quarks in 3, gluons in 8, and observable hadrons are color singlets.

Historically, color was introduced in the 1960s by Gell-Mann and independently by Zweig to resolve the spin-statistics puzzle and explain hadron multiplets. The gauge-field formulation of QCD was developed in the 1970s, and asymptotic freedom was discovered by Gross, Wilczek, and Politzer in 1973, establishing SU(3)_c as the correct description of strong interactions.