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
Pauli exclusion principle with respect to exchange of two identical particles the total wave function is antisymmetric for fermions, and symmetric for bosons. This means that if the space "and" spin co-ordinates of two identical particles are interchanged, then the wave function changes its sign for fermions and does not change for bosons. The Pauli exclusion principle describes the behavior of all fermions (particles with "half-integer spin"), while bosons (particles with "integer spin") are subject to other principles. Fermions include elementary particles such as quarks, electrons and neutrinos. Additionally, baryons such as protons and neutrons (subatomic particles composed from three quarks) and some