Gauge boson more complicated group "SU"(3) has eight generators, corresponding to the eight gluons. The three W and Z bosons correspond (roughly) to the three generators of "SU"(2) in GWS theory. For technical reasons involving gauge invariance, gauge bosons are described mathematically by field equations for massless particles. Therefore, at a naïve theoretical level, all gauge bosons are required to be massless, and the forces that they describe are required to be long-ranged. The conflict between this idea and experimental evidence that the weak and strong interactions have a very short range requires further theoretical insight. According to the Standard Model, the
Exchange operator Such motion is often not carried out in practice. Rather, the operation is treated as a "what if" similar to a parity inversion or time reversal operation. Consider two repeated operations of such a particle exchange: Therefore, formula_1 is not only unitary but also an operator square root of 1, which leaves the possibilities Both signs are realized in nature. Particles satisfying the case of +1 are called "bosons", and particles satisfying the case of −1 are called "fermions". The spin–statistics theorem dictates that all particles with integer spin are bosons whereas all particles with half-integer spin are fermions. The