Quantum chromodynamics observed particles make isospin and SU(3) multiplets. The approximate flavor symmetries do have associated gauge bosons, observed particles like the rho and the omega, but these particles are nothing like the gluons and they are not massless. They are emergent gauge bosons in an approximate string description of QCD. The dynamics of the quarks and gluons are controlled by the quantum chromodynamics Lagrangian. The gauge invariant QCD Lagrangian is where formula_1 is the quark field, a dynamical function of spacetime, in the fundamental representation of the SU(3) gauge group, indexed by formula_2; formula_3 is the gauge covariant derivative; the γ
W and Z bosons some extensions beyond the standard model they do.) The notation "x" = sin"θ" is used. W and Z bosons The W and Z bosons are together known as the weak or more generally as the intermediate vector bosons. These elementary particles mediate the weak interaction; the respective symbols are , , and . The W bosons have either a positive or negative electric charge of 1 elementary charge and are each other's antiparticles. The Z boson is electrically neutral and is its own antiparticle. The three particles have a spin of 1. The W bosons have a magnetic moment, but