Identical particles fermions, which do not share quantum states as described by the Pauli exclusion principle. Examples of bosons are photons, gluons, phonons, helium-4 nuclei and all mesons. Examples of fermions are electrons, neutrinos, quarks, protons, neutrons, and helium-3 nuclei. The fact that particles can be identical has important consequences in statistical mechanics. Calculations in statistical mechanics rely on probabilistic arguments, which are sensitive to whether or not the objects being studied are identical. As a result, identical particles exhibit markedly different statistical behaviour from distinguishable particles. For example, the indistinguishability of particles has been proposed as a solution to Gibbs' mixing
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