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
Force variables, whereas for two bosons (e.g. quanta of electromagnetic waves, photons) the correlation is strictly positive. Thus the notion "force" loses already part of its meaning. In modern particle physics, forces and the acceleration of particles are explained as a mathematical by-product of exchange of momentum-carrying gauge bosons. With the development of quantum field theory and general relativity, it was realized that force is a redundant concept arising from conservation of momentum (4-momentum in relativity and momentum of virtual particles in quantum electrodynamics). The conservation of momentum can be directly derived from the homogeneity or symmetry of space and so