A boson is a particle that obeys Bose–Einstein statistics: the quantum state of a system of identical bosons is unchanged when two particles are exchanged. In ordinary three-dimensional space, bosons have integer spin, such as 0, 1, or 2, whereas fermions have half-integer spin. Unlike fermions, identical bosons can occupy the same single-particle quantum state. Bosons include elementary particles, such as photons, and composite particles, such as helium-4 atoms. This classification concerns quantum behavior rather than whether a particle constitutes matter or carries a force. (damtp.cam.ac.uk)
Exchange symmetry and spin
In quantum mechanics, identical particles cannot be distinguished by permanent individual labels. For two identical bosons, their joint wave function satisfies
[ \Psi(x_1,x_2)=\Psi(x_2,x_1), ]
where each (x_i) represents the particle’s position and any relevant internal variables. For many bosons, the state is symmetric under every permutation of identical particles. A fermionic state instead changes sign when two particles are exchanged. These different exchange rules produce different ways of counting the available many-particle states. (damtp.cam.ac.uk)
The spin–statistics theorem connects this exchange behavior to spin within relativistic quantum field theory. Under the theorem’s standard assumptions, integer-spin particles obey bosonic statistics and half-integer-spin particles obey fermionic statistics. Spin is intrinsic angular momentum, not literal rotation of a small solid object. In the field description, bosonic creation operators commute, so creating two particles in opposite orders produces the same state. (damtp.cam.ac.uk)
Bosons are not subject to the Pauli exclusion principle. Consequently, there is no statistical restriction limiting a single-particle state to one boson. This does not require every boson in a system to occupy that state: interactions, confinement, and thermal conditions determine the actual distribution. Nor does sharing a quantum state mean that particles necessarily occupy one sharply defined spatial point. (damtp.cam.ac.uk)
Elementary bosons
The Standard Model contains spin-1 interaction carriers and a spin-0 Higgs boson. The photon carries the electromagnetic interaction; eight types of gluon carry the strong interaction; and the charged W bosons and neutral Z boson carry the weak interaction. These interaction carriers are called gauge bosons. Their bosonic classification follows from their quantum properties, while their different roles follow from the fields and interactions to which they belong. (home.web.cern.ch)
The Higgs boson is a scalar particle, meaning that its spin is zero. It is an excitation of the Higgs field, whose nonzero vacuum value participates in the mechanism giving mass to elementary particles. A new particle consistent with the Higgs boson was discovered at CERN in 2012, and subsequent measurements supported its spin-zero character. The Higgs is not one of the Standard Model’s spin-1 gauge bosons. (home.cern)
A graviton would be a spin-2 boson in a quantum description of gravity based on the corresponding field excitation. It is hypothetical and is not included in the Standard Model. Thus, “boson” is a broader category than “experimentally established force carrier.” (home.web.cern.ch)
Composite bosons and quasiparticles
A bound system containing an even number of fermionic constituents behaves as a boson when it can be treated as an intact particle. Its composite nature becomes important when experiments resolve its internal structure or supply enough energy to break it apart. For a neutral atom, the equal numbers of electrons and protons contribute an even total, so the parity of the neutron number determines whether the atom is bosonic or fermionic. (damtp.cam.ac.uk)
A neutral helium-4 atom contains two protons, two neutrons, and two electrons and is bosonic; helium-3 has one fewer neutron and is fermionic. Composite bosonic behavior also underlies the description of paired electrons in superconductivity. A Cooper pair contains two fermions, but overlapping pairs in a superconductor should not simply be pictured as a dilute gas of independent pointlike particles. (damtp.cam.ac.uk)
In solids, collective excitations can also obey bosonic statistics. A phonon is a quantum of lattice vibration, rather than an elementary particle traveling independently of the material. Treating vibrational modes as bosonic excitations makes it possible to calculate their thermal populations and contributions to a solid’s heat capacity. (damtp.cam.ac.uk)
Thermal statistics and condensation
For noninteracting bosons in thermal equilibrium, the mean occupation of a single-particle state with energy (\epsilon) is
[ \bar n(\epsilon)= \frac{1}{\exp[(\epsilon-\mu)/(k_{\mathrm B}T)]-1}, ]
where (\mu) is the chemical potential, (T) is temperature, and (k_{\mathrm B}) is the Boltzmann constant. The minus sign in the denominator distinguishes this distribution from the corresponding fermionic distribution. At low occupation, both approach the classical Boltzmann form. For equilibrium blackbody photons, the chemical potential is zero, and the bosonic distribution yields the Planck spectrum. (damtp.cam.ac.uk)
Under suitable conditions, a macroscopic fraction of bosons occupies the lowest-energy state, producing a Bose–Einstein condensate. Condensation in dilute atomic gases was achieved in 1995. Strongly interacting bosonic systems also exhibit collective quantum behavior: liquid helium-4 provides an important example of superfluidity. Its interactions mean that it cannot be understood simply as an ideal Bose gas with all atoms in one state. (damtp.cam.ac.uk)
Historical development
The name honors Satyendra Nath Bose, who introduced a new counting procedure for photons in 1924. Albert Einstein extended Bose’s approach to material particles in papers published in 1924 and 1925, predicting the condensation phenomenon. Their work established the statistical framework subsequently applied to particles classified as bosons. The experimental achievement of condensation in dilute alkali gases was recognized by the 2001 Nobel Prize in Physics, awarded jointly to Eric Cornell, Carl Wieman, and Wolfgang Ketterle. (nist.gov)