Fermion
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.
Fermions form one of the two fundamental classes of
subatomic particle, the other being bosons. All
subatomic particles must be one or the other. A
composite particle (hadron) may fall into either class
depending on its composition
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.[1]
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.[2]
Elementary fermions
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.[3]: 106 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 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.
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
Notes
1. Weiner, Richard M. (4 March
2013). "Spin-statistics-quantum
number connection and
supersymmetry" (https://journals.
aps.org/prd/abstract/10.1103/Ph
ysRevD.87.055003) . Physical
Review D. 87 (5): 055003–05.
arXiv:1302.0969 (https://arxiv.or
g/abs/1302.0969) .
Bibcode:2013PhRvD..87e5003W
(https://ui.adsabs.harvard.edu/ab
s/2013PhRvD..87e5003W) .
doi:10.1103/physrevd.87.055003
(https://doi.org/10.1103%2Fphysr
evd.87.055003) . ISSN 1550-7998
(https://search.worldcat.org/issn/
1550-7998) . S2CID 118571314
(https://api.semanticscholar.org/
CorpusID:118571314) . Retrieved
28 March 2022.
2. 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
3. T. Morii; C. S. Lim; S. N.
Mukherjee (1 January 2004). The
Physics of the Standard Model
and Beyond. World Scientific.
ISBN 978-981-279-560-1.
External links
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