Boson half-integer spin particles cannot be bosons and integer spin particles cannot be fermions. In large systems, the difference between bosonic and fermionic statistics is only apparent at large densities — when their wave functions overlap. At low densities, both types of statistics are well approximated by Maxwell–Boltzmann statistics, which is described by classical mechanics. All observed elementary particles are either fermions or bosons. The observed elementary bosons are all gauge bosons: photons, W and Z bosons, gluons, except the Higgs boson which is a scalar boson. Finally, many approaches to quantum gravity postulate a force carrier for gravity, the graviton,
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