In particle physics, a fermion is a particle that follows Fermi–Dirac statistics. Fermions have a half-odd-integer spin (spin ⁠1/2⁠, spin ⁠3/2⁠, etc.) and obey the Pauli exclusion principle. These particles include all quarks and leptons and all composite particles made of an odd number of these, such as all baryons and many atoms and nuclei. Fermions differ from bosons, which obey Bose–Einstein statistics.

Some fermions are elementary particles (such as electrons), and some are composite particles (such as protons). For example, according to the spin-statistics theorem in relativistic quantum field theory, particles with integer spin are bosons. In contrast, particles with half-integer spin are fermions.

In addition to the spin characteristic, fermions have another specific property: they possess conserved baryon or lepton quantum numbers. Therefore, what is usually referred to as the spin-statistics relation is, in fact, a spin statistics-quantum number relation.

As a consequence of the Pauli exclusion principle, only one fermion can occupy a particular quantum state at a given time. Suppose multiple fermions have the same spatial probability distribution. Then, at least one property of each fermion, such as its spin, must be different. Fermions are usually associated with matter, whereas bosons are generally force carrier particles. However, in the current state of particle physics, the distinction between the two concepts is unclear. Weakly interacting fermions can also display bosonic behavior under extreme conditions. For example, at low temperatures, fermions show superfluidity for uncharged particles and superconductivity for charged particles.

Composite fermions, such as protons and neutrons, are the key building blocks of everyday matter.

English theoretical physicist Paul Dirac coined the name fermion from the surname of Italian physicist Enrico Fermi.

Standard Model of particle physics
Elementary particles of the Standard Model
Background Particle physics Standard Model Quantum field theory Gauge theory Spontaneous symmetry breaking Higgs mechanism
Constituents Electroweak interaction Quantum chromodynamics CKM matrix Standard Model mathematics
Limitations Strong CP problem Hierarchy problem Neutrino oscillations Physics beyond the Standard Model
Scientists Rutherford Thomson Chadwick Bose Sudarshan Davis Jr Anderson Fermi Dirac Feynman Rubbia Gell-Mann Kendall Taylor Friedman Powell Anderson Glashow Iliopoulos Lederman Maiani Meer Cowan Nambu Chamberlain Cabibbo Schwartz Perl Majorana Weinberg Lee Ward Salam Kobayashi Maskawa Mills Yang Yukawa 't Hooft Veltman Gross Pais Pauli Politzer Reines Schwinger Wilczek Cronin Fitch Vleck Higgs Englert Brout Hagen Guralnik Kibble de Mayolo Lattes Zweig
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The Standard Model recognizes two types of elementary fermions: quarks and leptons. In all, the model distinguishes 24 different fermions. There are six quarks (up, down, strange, charm, bottom and top), and six leptons (electron, electron neutrino, muon, muon neutrino, tauon and tauon neutrino), along with the corresponding antiparticle of each of these.

Mathematically, there are many varieties of fermions, with the three most common types being:

• Weyl fermions (massless),
• Dirac fermions (massive), and
• Majorana fermions (each its own antiparticle).

Most Standard Model fermions are believed to be Dirac fermions, although it is unknown at this time whether the neutrinos are Dirac or Majorana fermions (or both). Dirac fermions can be treated as a combination of two Weyl fermions. In July 2015, Weyl fermions have been experimentally realized in Weyl semimetals.

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 odd number of fermions is itself a fermion. It will have half-integer spin.

Examples include the following:

• A baryon, such as the proton or neutron, contains three fermionic quarks.
• The nucleus of a carbon-13 atom contains six protons and seven neutrons.
• The atom helium-3 (He) consists of two protons, one neutron, and two electrons. The deuterium atom consists of one proton, one neutron, and one electron.

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) distances. At proximity, where spatial structure begins to be important, a composite particle (or system) behaves according to its constituent makeup.

Fermions can exhibit bosonic behavior when they become loosely bound in pairs. This is the origin of superconductivity and the superfluidity of helium-3: in superconducting materials, electrons interact through the exchange of phonons, forming Cooper pairs, while in helium-3, Cooper pairs are formed via spin fluctuations.

The quasiparticles of the fractional quantum Hall effect are also known as composite fermions; they consist of electrons with an even number of quantized vortices attached to them.