Color charge is the conserved quantum number that couples to the \(SU(3)_c\) gauge field of QCD, the strong-interaction analogue of electric charge in QED. Unlike electric charge, which is a single number, color is a non-abelian charge: it takes values in the (eight-dimensional) Lie algebra of \(SU(3)\), and it comes in three basis "colors" conventionally called red, green and blue.
- Quarks carry color in the fundamental representation \(\mathbf{3}\) (three colors); antiquarks in \(\overline{\mathbf 3}\).
- Gluons carry color in the adjoint representation \(\mathbf 8\) — they are themselves charged, which is the defining feature of a non-abelian theory.
The generators \(T^a\) (\(3\times3\) hermitian matrices) act on the color index of the quark field \(\psi_a\), \(a=1,2,3\).
Color was postulated to rescue the Pauli exclusion principle. Consider the baryons
each made of three identical spin-\(\tfrac12\) quarks with parallel spins in a spatially symmetric ground state. The total wavefunction (spatial \(\times\) spin \(\times\) flavour) is symmetric, which would violate Fermi statistics. Assigning each quark a new three-valued color label and requiring the physical state to be totally antisymmetric in color,
restores antisymmetry. See Deepseek_color_charge_requirement for the detailed argument.
Only color-singlet combinations appear as physical states: mesons \(\bar q_a q^a\) and baryons \(\epsilon^{abc}q_a q_b q_c\). Isolated color charge is never observed — the linear rise of the static potential \(V(r)\sim\sigma r\) means separating color sources costs unbounded energy. Experimentally, color is confirmed by the ratio \(R=\sigma(e^+e^-\to\text{hadrons})/\sigma(e^+e^-\to\mu^+\mu^-)\), which is enhanced by the factor \(N_c=3\).