Fermion

Not to be confused withfermium.

Fermions form one of the two fundamental classes ofsubatomic particle,the other beingbosons.All subatomic particles must be one or the other. A composite particle (hadron) may fall into either class depending on its composition

Inparticle physics,afermionis a particle that followsFermi–Dirac statistics.Fermions have a half-odd-integer spin (spin⁠1/2⁠,spin⁠3/2⁠,etc.) and obey thePauli exclusion principle.These particles include allquarksandleptonsand allcomposite particlesmade of anodd numberof these, such as allbaryonsand manyatomsandnuclei.Fermions differ frombosons,which obeyBose–Einstein statistics.

Some fermions areelementary particles(such aselectrons), and some arecomposite particles(such asprotons). For example, according to thespin-statistics theoreminrelativisticquantum field theory,particles withintegerspinarebosons.In contrast, particles withhalf-integerspin are fermions.

In addition to the spin characteristic, fermions have another specific property: they possess conserved baryon or leptonquantum 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 particularquantum stateat a given time. Suppose multiple fermions have the same spatialprobability distribution.Then, at least one property of each fermion, such as its spin, must be different. Fermions are usually associated withmatter,whereas bosons are generallyforce carrierparticles. However, in the current state of particle physics, the distinction between the two concepts is unclear.Weakly interactingfermions can also display bosonic behavior under extreme conditions. For example, at low temperatures, fermions showsuperfluidityfor uncharged particles andsuperconductivityfor charged particles.

Composite fermions, such as protons andneutrons,are the key building blocks ofeveryday matter.

English theoretical physicistPaul Diraccoined the name fermion from the surname of Italian physicistEnrico Fermi.

Elementary fermions

TheStandard Modelrecognizes two types of elementary fermions:quarksandleptons.In all, the model distinguishes 24 different fermions. There are six quarks (up,down,strange,charm,bottomandtop), and six leptons (electron,electron neutrino,muon,muon neutrino,tauonandtauon neutrino), along with the correspondingantiparticleof 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 theneutrinosare 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 inWeyl semimetals.

Composite fermions

See also:List of particles § Composite particles

Composite particles (such ashadrons,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 acarbon-13atom contains six protons and seven neutrons.
• The atomhelium-3(³He) consists of two protons, one neutron, and two electrons. Thedeuteriumatom 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 thesuperfluidityof helium-3: in superconducting materials, electrons interact through the exchange ofphonons,formingCooper pairs,while in helium-3, Cooper pairs are formed via spin fluctuations.

The quasiparticles of thefractional quantum Hall effectare also known ascomposite fermions;they consist of electrons with an even number of quantized vortices attached to them.

See also

• Anyon,2D quasiparticles
• Chirality (physics),left-handed and right-handed
• Fermionic condensate
• Weyl semimetal
• Fermionic field
• Identical particles
• Kogut–Susskind fermion,a type of lattice fermion
• Majorana fermion,each its own antiparticle
• Parastatistics
• Skyrmion,a hypothetical particle