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) an ...

, a fermion is a particle that follows

Fermi–Dirac statistics Fermi–Dirac statistics (F–D statistics) is a type of quantum statistics that applies to the physics of a system consisting of many non-interacting, identical particles that obey the Pauli exclusion principle. A result is the Fermi–Dirac d ...

. Generally, it has a half-odd-integer spin: spin , spin , etc. In addition, these particles obey the

Pauli exclusion principle In quantum mechanics, the Pauli exclusion principle states that two or more identical particles with half-integer spins (i.e. fermions) cannot occupy the same quantum state within a quantum system simultaneously. This principle was formula ...

. 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 commonly ...

s and

lepton In particle physics, a lepton is an elementary particle of half-integer spin (spin ) that does not undergo strong interactions. Two main classes of leptons exist: charged leptons (also known as the electron-like leptons or muons), and neutr ...

s and all

composite particle This is a list of known and hypothesized particles. Elementary particles Elementary particles are particles with no measurable internal structure; that is, it is unknown whether they are composed of other particles. They are the fundamental ob ...

s made of an

odd number In mathematics, parity is the property of an integer of whether it is even or odd. An integer is even if it is a multiple of two, and odd if it is not.. For example, −4, 0, 82 are even because \begin -2 \cdot 2 &= -4 \\ 0 \cdot 2 &= 0 \\ 41 ...

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 classifie ...

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, a ...

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 spi ...

s, which obey

Bose–Einstein statistics In quantum statistics, Bose–Einstein statistics (B–E statistics) describes one of two possible ways in which a collection of non-interacting, indistinguishable particles may occupy a set of available discrete energy states at thermodynamic ...

. Some fermions are

elementary particle In particle physics, an elementary particle or fundamental particle is a subatomic particle that is not composed of other particles. Particles currently thought to be elementary include electrons, the fundamental fermions ( quarks, leptons, ...

s (such as

electron The electron ( or ) 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 particles because they have n ...

s), and some are

s (such as

proton A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' elementary charge. Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron mass ...

s). 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 and ...

, 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 languag ...

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 ...

are

s. In contrast, particles with

half-integer In mathematics, a half-integer is a number of the form :n + \tfrac, where n is an whole number. For example, :, , , 8.5 are all ''half-integers''. The name "half-integer" is perhaps misleading, as the set may be misunderstood to include numbers ...

spin are fermions. In addition to the spin characteristic, fermions have another specific property: they possess conserved baryon or lepton

quantum number In quantum physics and chemistry, quantum numbers describe values of conserved quantities in the dynamics of a quantum system. Quantum numbers correspond to eigenvalues of operators that commute with the Hamiltonian—quantities that can ...

s. 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 i ...

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 part ...

, whereas bosons are generally

force carrier In quantum field theory, a force carrier, also known as messenger particle or intermediate particle, is a type of particle that gives rise to forces between other particles. These particles serve as the quanta of a particular kind of physical fi ...

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 ...

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. Unlike ...

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 atomic nucleus, nuclei of atoms. Since protons and ...

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 Univer ...

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. It ...

recognizes two types of elementary fermions:

s and

s. In all, the model distinguishes 24 different fermions. There are six quarks ( up, down, strange,

charm Charm may refer to: Social science * Charisma, a person or thing's pronounced ability to attract others * Superficial charm, flattery, telling people what they want to hear Science and technology * Charm quark, a type of elementary particle * Ch ...

, bottom and top), and six leptons (

electron neutrino The electron neutrino () is an elementary particle which has zero electric charge and a spin of . Together with the electron, it forms the first generation of leptons, hence the name electron neutrino. It was first hypothesized by Wolfgang Pauli ...

muon A muon ( ; from the Greek letter mu (μ) used to represent it) is an elementary particle similar to the electron, with an electric charge of −1 '' e'' and a spin of , but with a much greater mass. It is classified as a lepton. As w ...

, muon neutrino,

tauon The tau (), also called the tau lepton, tau particle, tauon or tau electron, is an elementary particle similar to the electron, with negative electric charge and a spin of . Like the electron, the muon, and the three neutrinos, the tau is a l ...

and tauon neutrino), along with the corresponding

antiparticle In particle physics, every type of particle is associated with an antiparticle with the same mass but with opposite physical charges (such as electric charge). For example, the antiparticle of the electron is the positron (also known as an antie ...

of each of these. Mathematically, there are many varieties of fermions, with the three most common types being: * Weyl fermions (massless), *

Dirac fermion In physics, a Dirac fermion is a spin-½ particle (a fermion) which is different from its antiparticle. The vast majority of fermions – perhaps all – fall under this category. Description In particle physics, all fermions in the standard mo ...

s (massive), and *

Majorana fermion A Majorana fermion (, uploaded 19 April 2013, retrieved 5 October 2014; and also based on the pronunciation of physicist's name.), also referred to as a Majorana particle, is a fermion that is its own antiparticle. They were hypothesised by ...

s (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

hadron In particle physics, a hadron (; grc, ἁδρός, hadrós; "stout, thick") is a composite subatomic particle made of two or more quarks held together by the strong interaction. They are analogous to molecules that are held together by the ...

s, 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 Carbon-13 (13C) is a natural, stable isotope of carbon with a nucleus containing six protons and seven neutrons. As one of the environmental isotopes, it makes up about 1.1% of all natural carbon on Earth. Detection by mass spectrometry A mas ...

atom contains six protons and seven neutrons. *The atom

helium-3 Helium-3 (3He see also helion) is a light, stable isotope of helium with two protons and one neutron (the most common isotope, helium-4, having two protons and two neutrons in contrast). Other than protium (ordinary hydrogen), helium-3 is the ...

(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 isotopes of hydrogen (the other being protium, or hydrogen-1). The nucleus of a deuterium atom, called a deuteron, contains one proton and one ...

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 mechani ...

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 A composite fermion is the topological bound state of an electron and an even number of quantized vortices, sometimes visually pictured as the bound state of an electron and, attached, an even number of magnetic flux quanta. Composite fermions we ...

; they consist of electrons with an even number of quantized vortices attached to them.

Notes

External links

{{Authority control Quantum field theory Enrico Fermi

Elementary fermions

Composite fermions

See also

Notes

External links