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In
particle physics Particle physics or high energy physics is the study of fundamental particles and forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) and ...
, a fermion is a particle that follows Fermi–Dirac statistics. Generally, it has a half-odd-integer spin:
spin Spin or spinning most often refers to: * Spinning (textiles), the creation of yarn or thread by twisting fibers together, traditionally by hand spinning * Spin, the rotation of an object around a central axis * Spin (propaganda), an intentionally ...
,
spin Spin or spinning most often refers to: * Spinning (textiles), the creation of yarn or thread by twisting fibers together, traditionally by hand spinning * Spin, the rotation of an object around a central axis * Spin (propaganda), an intentionally ...
, etc. In addition, these particles obey the Pauli exclusion principle. Fermions include all
quark A quark () is a type of elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. All common ...
s and leptons and all composite particles made of an odd number of these, such as all
baryon In particle physics, a baryon is a type of composite subatomic particle which contains an odd number of valence quarks (at least 3). Baryons belong to the hadron family of particles; hadrons are composed of quarks. Baryons are also classi ...
s and many
atom Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, gas ...
s and nuclei. Fermions differ from
boson In particle physics, a boson ( ) is a subatomic particle whose spin quantum number has an integer value (0,1,2 ...). Bosons form one of the two fundamental classes of subatomic particle, the other being fermions, which have odd half-integer s ...
s, which obey Bose–Einstein statistics. Some fermions are elementary particles (such as
electron The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary partic ...
s), and some are composite particles (such as protons). For example, according to the spin-statistics theorem in relativistic
quantum field theory In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles a ...
, particles with
integer An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign ( −1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the language ...
spin are
boson In particle physics, a boson ( ) is a subatomic particle whose spin quantum number has an integer value (0,1,2 ...). Bosons form one of the two fundamental classes of subatomic particle, the other being fermions, which have odd half-integer s ...
s. 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 In quantum physics, a quantum state is a mathematical entity that provides a probability distribution for the outcomes of each possible measurement on a system. Knowledge of the quantum state together with the rules for the system's evolution in ...
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 In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, which are made up of interacting subatomic par ...
, 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 Superfluidity is the characteristic property of a fluid with zero viscosity which therefore flows without any loss of kinetic energy. When stirred, a superfluid forms vortices that continue to rotate indefinitely. Superfluidity occurs in two i ...
for uncharged particles and
superconductivity Superconductivity is a set of physical properties observed in certain materials where electrical resistance vanishes and magnetic flux fields are expelled from the material. Any material exhibiting these properties is a superconductor. Unlik ...
for charged particles. Composite fermions, such as protons and
neutron The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the nuclei of atoms. Since protons and neutrons behav ...
s, are the key building blocks of everyday matter. English theoretical physicist
Paul Dirac Paul Adrien Maurice Dirac (; 8 August 1902 – 20 October 1984) was an English theoretical physicist who is regarded as one of the most significant physicists of the 20th century. He was the Lucasian Professor of Mathematics at the Unive ...
coined the name fermion from the surname of Italian physicist
Enrico Fermi Enrico Fermi (; 29 September 1901 – 28 November 1954) was an Italian (later naturalized American) physicist and the creator of the world's first nuclear reactor, the Chicago Pile-1. He has been called the "architect of the nuclear age" an ...
.Notes on Dirac's lecture ''Developments in Atomic Theory'' at Le Palais de la Découverte, 6 December 1945, UKNATARCHI Dirac Papers BW83/2/257889. See note 64 on page 331 in "The Strangest Man: The Hidden Life of Paul Dirac, Mystic of the Atom" by Graham Farmelo


Elementary fermions

The
Standard Model The Standard Model of particle physics is the theory describing three of the four known fundamental forces ( electromagnetic, weak and strong interactions - excluding gravity) in the universe and classifying all known elementary particles. I ...
recognizes two types of elementary fermions:
quark A quark () is a type of elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. All common ...
s and leptons. In all, the model distinguishes 24 different fermions. There are six quarks ( up,
down Down most often refers to: * Down, the relative direction opposed to up * Down (gridiron football), in American/Canadian football, a period when one play takes place * Down feather, a soft bird feather used in bedding and clothing * Downland, a ty ...
, strange, charm, bottom and top), and six leptons (
electron The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary partic ...
, 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
neutrino A neutrino ( ; denoted by the Greek letter ) is a fermion (an elementary particle with spin of ) that interacts only via the weak interaction and gravity. The neutrino is so named because it is electrically neutral and because its rest mass ...
s 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 fermions

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 (3He) consists of two protons, one neutron, and two electrons. The
deuterium Deuterium (or hydrogen-2, symbol or deuterium, also known as heavy hydrogen) is one of two Stable isotope ratio, stable isotopes of hydrogen (the other being Hydrogen atom, protium, or hydrogen-1). The atomic nucleus, nucleus of a deuterium ato ...
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
phonon In physics, a phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter, specifically in solids and some liquids. A type of quasiparticle, a phonon is an excited state in the quantum mechanical ...
s, forming Cooper pairs, while in helium-3, Cooper pairs are formed via spin fluctuations. The quasiparticles of the
fractional quantum Hall effect The fractional quantum Hall effect (FQHE) is a physical phenomenon in which the Hall conductance of 2-dimensional (2D) electrons shows precisely quantized plateaus at fractional values of e^2/h. It is a property of a collective state in which elec ...
are also known as composite fermions; they consist of electrons with an even number of quantized vortices attached to them.


See also

*
Anyon In physics, an anyon is a type of quasiparticle that occurs only in two-dimensional systems, with properties much less restricted than the two kinds of standard elementary particles, fermions and bosons. In general, the operation of exchan ...
, 2D quasiparticles * Chirality (physics), left-handed and right-handed * Fermionic condensate * Weyl semimetal * Fermionic field * Identical particles *
Kogut–Susskind fermion In lattice field theory, staggered fermions (also known as Kogut–Susskind fermions) are a fermion discretization that reduces the number of fermion doublers from sixteen to four. They are one of the fastest lattice fermions when it comes to si ...
, a type of lattice fermion * Majorana fermion, each its own antiparticle * Parastatistics * Skyrmion, a hypothetical particle


Notes


External links

{{Authority control Quantum field theory Enrico Fermi