Abelian group non-Abelian groups non-Abelian gauge theories Quantum chromodynamics SU(3) quark gluon group vector field gauge theory symmetry Lagrangian gauge symmetry vector Dirac field gauge bosons Dirac fields gauge boson U(1) field action vector fields strong interaction fields
U(1) is an Abelian group, meaning that the result is the same regardless of the order in which its elements are applied. QFTs can also be built on non-Abelian groups, giving rise to non-Abelian gauge theories (also known as Yang–Mills theories). Quantum chromodynamics, which describes the strong interaction, is a non-Abelian gauge theory with an SU(3) gauge symmetry. It contains three Dirac fields ψ, i = 1,2,3 representing quark fields as well as eight vector fields A, a = 1,...,8 representing gluon fields, which are the SU(3) gauge bosons. The QCD Lagrangian density is:
