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,
Introduction to gauge theory the course of the 20th century, physicists gradually realized that all forces (fundamental interactions) arise from the constraints imposed by "local" gauge symmetries, in which case the transformations vary from point to point in space and time. Perturbative quantum field theory (usually employed for scattering theory) describes forces in terms of force-mediating particles called gauge bosons. The nature of these particles is determined by the nature of the gauge transformations. The culmination of these efforts is the Standard Model, a quantum field theory that accurately predicts all of the fundamental interactions except gravity. The earliest field theory having a gauge