In quantum mechanics, a boson (/ˈboʊsɒn/,^[3] /ˈboʊzɒn/^[4]) is a particle that follows Bose–Einstein statistics. Bosons make up one of the two classes of particles, the other being fermions.^[5] The name boson was coined by Paul Dirac^[6][7] to commemorate the contribution of Indian physicist and professor of physics at University of Calcutta and at University of Dhaka, Satyendra Nath Bose^[8][9] in developing, with Albert Einstein, Bose–Einstein statistics—which theorizes the characteristics of elementary particles.^[10]

Examples of bosons include fundamental particles such as photons, gluons, and W and Z bosons (the four force-carrying gauge bosons of the Standard Model), the recently discovered Higgs boson, and the hypothetical graviton of quantum gravity. Some composite particles are also bosons, such as mesons and stable nuclei of even mass number such as deuterium (with one proton and one neutron, atomic mass number = 2), helium-4, or lead-208;^[1] as well as some quasiparticles (e.g. Cooper pairs, plasmons, and phonons).^{[11] []}

An important characteristic of bosons is that their statistics do not restrict the number of them that occupy the same quantum state. This property is exemplified by helium-4 when it is cooled to become a superfluid.^[12] Unlike bosons, two identical fermions cannot occupy the same quantum space. Whereas the elementary particles that make up matter (i.e. leptons and quarks) are fermions, the elementary bosons are force carriers that function as the 'glue' holding matter together.^[13] This property holds for all particles with integer spin (s = 0, 1, 2, etc.) as a consequence of the spin–statistics theorem. When a gas of Bose particles is cooled down to temperatures very close to absolute zero, then the kinetic energy of the particles decreases to a negligible amount, and they condense into the lowest energy level state. This state is called a Bose–Einstein condensate. This property is also the explanation for superfluidity.

Bosons may be either elementary, like photons, or composite, like mesons.

While most bosons are composite particles, in the Standard Model of Particle Physics there are five bosons which are elementary:

There may be a sixth tensor boson (spin=2), the graviton (G), that would be the force-carrier for gravity. It remains a hypothetical elementary particle since all attempts so far to incorporate gravitation into the Standard Model have failed. If the graviton does exist, it must be a boson, and could conceivably be a gauge boson.^[2]

Composite bosons, such as helium nuclei, are important in superfluidity and other applications of Bose–Einstein condensates.

Bosons differ from fermions, which obey Fermi–Dirac statistics. Two or more identical fermions cannot occupy the same quantum state (see Pauli exclusion principle), and they are sometimes said to be the constituents of ordinary "rigid" matter. Unlike those, instances of a boson have no quantum-mechanical obstruction to occupy the same state. Bosons are often (although not necessarily) force carrier particles, including composite bosons such as mesons. Force carriers are also said to be the particles that transmit interactions, or the constituents of radiation.

The Bose–Einstein statistics implies that, when one swaps two bosons (of the same species), the wavefunction of the system is unchanged.^[14] The quantum fields of bosons are bosonic fields, obeying canonical commutation relations.

The properties of lasers and masers, superfluid helium-4 and Bose–Einstein condensates are all consequences of statistics of bosons. Another result is that the spectrum of a photon gas in thermal equilibrium is a Planck spectrum, one example of which is black-body radiation; another is the thermal radiation of the opaque early Universe seen today as microwave background radiation. Interactions between elementary particles are called fundamental interactions. The fundamental interactions of virtual bosons with real particles result in all forces we know.

All known elementary and composite particles are bosons or fermions, depending on their spin: Particles with half-integer spin are fermions; particles with integer spin are bosons. In the framework of nonrelativistic quantum mechanics, this is a purely empirical observation. In relativistic quantum field theory, the spin–statistics theorem shows that half-integer spin particles cannot be bosons and integer spin particles cannot be fermions.^[15]

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, which is a boson of spin plus or minus two.

Composite particles (such as hadrons, nuclei, and atoms) can be bosons or fermions depending on their constituents. More precisely, because of the relation between spin and statistics, a particle containing an even number of fermions is a boson, since it has integer spin.

Examples include the following:

The number of bosons within a composite particle made up of simple particles bound with a potential has no effect on whether it is a boson or a fermion.

Bose–Einstein statistics encourages identical bosons to crowd into one quantum state, but not any state is necessarily convenient for it. Aside of statistics, bosons can interact – for example, helium-4 atoms are repulsed by intermolecular force on a very close approach, and if one hypothesizes their condensation in a spatially-localized state, then gains from the statistics cannot overcome a prohibitive force potential. A spatially-delocalized state (i.e. with low |ψ(x)|) is preferable: if the number density of the condensate is about the same as in ordinary liquid or solid state, then the repulsive potential for the N-particle condensate in such state can be no higher than for a liquid or a crystalline lattice of the same N particles described without quantum statistics. Thus, Bose–Einstein statistics for a material particle is not a mechanism to bypass physical restrictions on the density of the corresponding substance, and superfluid liquid helium has a density comparable to the density of ordinary liquid matter. Spatially-delocalized states also permit for a low momentum according to the uncertainty principle, hence for low kinetic energy; this is why superfluidity and superconductivity are usually observed in low temperatures.

Photons do not interact with themselves and hence do not experience this difference in states where to crowd (see squeezed coherent state).