Boson

For other uses, see Boson (disambiguation).

In particle physics, bosons (/ˈboʊsɒn/), /ˈboʊzɒn/) comprise one of two classes of elementary particles, the other being fermions. The name boson was coined by Paul Dirac to commemorate the contribution of Satyendra Nath Bose in developing, with Einstein, Bose–Einstein statistics—which theorizes the characteristics of elementary particles. Examples of bosons include fundamental particles (i.e., Higgs boson, the four force-carrying gauge bosons of the Standard Model, and the still-theoretical graviton of quantum gravity); composite particles (i.e., mesons, stable nuclei of even mass number, e.g., deuterium, helium-4, lead-208); and quasiparticles (e.g. Cooper pairs).

An important characteristic of bosons is that there is no limit to the number that can occupy the same quantum state. This property is evidenced, among other areas, in helium-4 when it is cooled to become a superfluid. In contrast, two 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. There is a deep relationship between this property and integer spin (s = 0, 1, 2 etc.).^{[citation needed]}

Properties of bosons

Bosons contrast with fermions, which obey Fermi–Dirac statistics. Two or more fermions cannot occupy the same quantum state (see Pauli exclusion principle).

Since bosons with the same energy can occupy the same place in space, bosons are often force carrier particles. In contrast, fermions are usually associated with matter (although in quantum physics the distinction between the two concepts is not clear cut).

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

All observed bosons have integer spin, as opposed to fermions, which have half-integer spin. This is in accordance with the spin-statistics theorem, which states that in any reasonable relativistic quantum field theory, particles with integer spin are bosons, while particles with half-integer spin are fermions.

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

• the four gauge bosons (γ · g · Z · W±)
• the Higgs boson (H0).

Additionally, the graviton (G), a hypothetical elementary particle not incorporated in the Standard Model, if it exists, must be a boson, and could conceivably be a gauge boson.

Composite bosons are important in superfluidity and other applications of Bose–Einstein condensates.

Definition and basic properties

By definition, bosons are particles which obey Bose–Einstein statistics: when one swaps two bosons (of the same species), the wavefunction of the system is unchanged. Fermions, on the other hand, obey Fermi–Dirac statistics and the Pauli exclusion principle: two fermions cannot occupy the same quantum state, resulting in a "rigidity" or "stiffness" of matter which includes fermions. Thus fermions are sometimes said to be the constituents of matter, while bosons are said to be the particles that transmit interactions (force carriers), or the constituents of radiation. 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. However, 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.

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.

Elementary bosons

See also: List of particles: Bosons - Particles described by Bose–Einstein statistics

All observed elementary particles are either fermions or bosons. The observed elementary bosons are all gauge bosons: photons, W and Z bosons and gluons.

• Photons are the force carriers of the electromagnetic field.
• W and Z bosons are the force carriers which mediate the weak force.
• Gluons are the fundamental force carriers underlying the strong force.

In addition, the standard model postulates the existence of Higgs bosons, which give other particles their mass via the Higgs mechanism. As of July 2012, scientists at the LHC believe they may have observed these particles, although further tests are needed to confirm this discovery. Since the Higgs field is a scalar field, the Higgs boson has no spin. The Higgs boson is also its own antiparticle and is CP-even, and has zero electric and color charge.

Finally, many approaches to quantum gravity postulate a force carrier for gravity, the graviton, which is a boson of spin 2.

Composite bosons

See also: List of particles: Composite particles

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:

• Any meson, since mesons contain one quark and one antiquark.
• The nucleus of a carbon-12 atom, which contains 6 protons and 6 neutrons.
• The helium-4 atom, consisting of 2 protons, 2 neutrons and 2 electrons.

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.

Fermionic or bosonic behavior of a composite particle (or system) is only seen at large (compared to size of the system) distance. At proximity, where spatial structure begins to be important, a composite particle (or system) behaves according to its constituent makeup. For example, two atoms of helium-4 cannot share the same space if it is comparable in size to that of the inner structure of the helium atom itself (~10⁻¹⁰ m)—despite bosonic properties of the helium-4 atoms. Thus, liquid helium has finite density comparable to the density of ordinary liquid matter.

See also

• Anyon
• Bose gas
• Identical particles
• Parastatistics
• Cooper pairs