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,
Gauge theory Lagrangian. In the quantized version of the obtained classical field theory, the quanta of the gauge field "A"("x") are called gauge bosons. The interpretation of the interaction Lagrangian in quantum field theory is of scalar bosons interacting by the exchange of these gauge bosons. The picture of a classical gauge theory developed in the previous section is almost complete, except for the fact that to define the covariant derivatives "D", one needs to know the value of the gauge field formula_29 at all space-time points. Instead of manually specifying the values of this field, it can be given as the