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
Elementary particle of elementary particles by hypothesizing that each known particle associates with a "shadow" partner far more massive, although all such superpartners remain undiscovered. Meanwhile, an elementary boson mediating gravitation—the graviton—remains hypothetical. All elementary particles are—depending on their "spin"—either bosons or fermions. These are differentiated via the spin–statistics theorem of quantum statistics. Particles of "half-integer" spin exhibit Fermi–Dirac statistics and are fermions. Particles of "integer" spin, in other words full-integer, exhibit Bose–Einstein statistics and are bosons. In the Standard Model, elementary particles are represented for predictive utility as point particles. Though extremely successful, the Standard Model is limited to the microcosm