Physics:Quantum fermion: Difference between revisions

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{{Short description|Type of subatomic particle}}
{{Short description|Half-integer-spin quantum particle obeying Fermi-Dirac statistics}}


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{{Quantum matter backlink|Particles}}
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A '''fermion''' is a [[Physics:Quantum particle|subatomic particle]] that follows [[Fermi–Dirac statistics]]. Fermions have [[half-integer]] [[Physics:Quantum spin|spin]] and obey the [[Physics:Quantum Pauli exclusion principle|Pauli exclusion principle]]. These particles include all [[Physics:Quantum quark|quarks]], [[Physics:Quantum lepton|leptons]], and composite particles made from an odd number of fermions, such as [[Physics:Quantum proton|protons]], [[Physics:Quantum neutron|neutrons]], many nuclei, and many atoms.
A '''quantum fermion''' is a particle with half-integer spin that obeys Fermi-Dirac statistics. Fermions have antisymmetric many-particle wavefunctions, so identical fermions cannot occupy the same one-particle quantum state. This rule gives matter much of its structure, from atomic shells to degenerate stars.<ref name="pauli1940">{{cite journal |last=Pauli |first=Wolfgang |title=The Connection Between Spin and Statistics |journal=Physical Review |year=1940 |volume=58 |issue=8 |pages=716-722 |doi=10.1103/PhysRev.58.716}}</ref><ref name="pdg">{{cite journal |author=Particle Data Group |title=Review of Particle Physics |journal=Progress of Theoretical and Experimental Physics |year=2022 |volume=2022 |issue=8 |pages=083C01 |doi=10.1093/ptep/ptac097}}</ref>
 
Fermions differ from [[Physics:Quantum boson|bosons]], which obey Bose–Einstein statistics. In relativistic [[Physics:Quantum field theory|quantum field theory]], particles with integer spin behave as bosons, while particles with half-integer spin behave as fermions.
 
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== Spin and statistics ==
The spin-statistics connection links half-integer spin with fermionic exchange behavior in relativistic quantum theory. Exchanging two identical fermions changes the sign of the many-body wavefunction. The resulting Pauli exclusion principle is not an ordinary force; it is a constraint on the allowed quantum states.<ref name="peskin">{{cite book |last1=Peskin |first1=Michael E. |last2=Schroeder |first2=Daniel V. |title=An Introduction to Quantum Field Theory |publisher=Addison-Wesley |year=1995 |isbn=978-0-201-50397-5}}</ref>


== Description ==
== Elementary and composite fermions ==
Fermions possess conserved baryon or lepton quantum numbers in addition to their spin properties. Because of the Pauli exclusion principle, no two identical fermions can occupy exactly the same quantum state at the same time.<ref>{{cite journal |last=Weiner |first=Richard M. |date=4 March 2013 |title=Spin-statistics-quantum number connection and supersymmetry |url=https://journals.aps.org/prd/abstract/10.1103/PhysRevD.87.055003 |journal=Physical Review D |volume=87 |issue=5 |pages=055003–05 |arxiv=1302.0969 |bibcode=2013PhRvD..87e5003W |doi=10.1103/physrevd.87.055003 |issn=1550-7998 |access-date=28 March 2022 |s2cid=118571314}}</ref>
Elementary fermions include [[Physics:Quantum quark|quarks]] and [[Physics:Quantum lepton|leptons]]. Composite systems can also behave as fermions when their total spin is half-integer, as in protons, neutrons, many nuclei, atoms, and quasiparticle excitations in condensed matter.
 
If several fermions occupy the same spatial region, at least one quantum property, such as spin orientation, must differ between them. This exclusion principle is responsible for much of the structure and stability of ordinary matter, including electron shells in atoms.
 
Fermions are generally associated with matter, while bosons are usually associated with force mediation. However, under special conditions fermions can collectively display bosonic behaviour. Examples include superconductivity and superfluidity.
 
Composite fermions such as protons and neutrons are the primary building blocks of ordinary baryonic matter.
 
The term ''fermion'' was introduced by English physicist [[Biography:Paul Dirac|Paul Dirac]] in honour of Italian physicist [[Biography:Enrico Fermi|Enrico Fermi]].<ref>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</ref>
 
== Elementary fermions ==
{{Standard model of particle physics|cTopic=[[Elementary particle]]s}}
 
The [[Physics:Quantum Standard Model|Standard Model]] recognizes two families of elementary fermions:
 
* [[Physics:Quantum quark|quarks]]
* [[Physics:Quantum lepton|leptons]]
 
In total there are 24 elementary fermions when antiparticles are included.
 
=== Quarks ===
The six known quarks are:
 
* [[Physics:Quantum up quark|up quark]]
* [[Physics:Quantum down quark|down quark]]
* [[Physics:Quantum strange quark|strange quark]]
* [[Physics:Quantum charm quark|charm quark]]
* [[Physics:Quantum bottom quark|bottom quark]]
* [[Physics:Quantum top quark|top quark]]
 
Quarks carry color charge and participate in the strong interaction. They combine to form hadrons such as protons and neutrons.
 
=== Leptons ===
The six leptons are:
 
* [[Physics:Quantum atoms/electron|electron]]
* [[Physics:Quantum electron neutrino|electron neutrino]]
* [[Physics:Quantum muon|muon]]
* [[Physics:Quantum muon neutrino|muon neutrino]]
* [[Physics:Quantum tau|tau]]
* [[Physics:Quantum tau neutrino|tau neutrino]]
 
Leptons do not participate in the strong interaction. Neutrinos interact only weakly and gravitationally.
 
=== Types of fermions ===
Mathematically, several forms of fermions are known:
 
* [[Physics:Quantum Weyl fermion|Weyl fermions]] (massless)
* [[Physics:Quantum Dirac fermion|Dirac fermions]] (massive)
* [[Physics:Quantum Majorana fermion|Majorana fermions]] (their own antiparticles)
 
Most Standard Model fermions are believed to behave as Dirac fermions, although the exact nature of neutrinos remains uncertain.<ref name="MoriiLim2004">{{cite book |last1=Morii |first1=T. |title=The Physics of the Standard Model and Beyond |last2=Lim |first2=C. S. |last3=Mukherjee |first3=S. N. |date=1 January 2004 |publisher=[[World Scientific]] |isbn=978-981-279-560-1}}</ref>{{rp|106}}
 
In 2015, Weyl fermions were experimentally realized in [[Physics:Quantum Weyl semimetal|Weyl semimetals]].
 
== Composite fermions ==
Composite particles can behave as fermions or bosons depending on the number of constituent fermions.
 
Examples include:
 
* a proton, containing three quarks
* a neutron, containing three quarks
* the nucleus of carbon-13
* helium-3 atoms
* deuterium atoms
 
A composite particle containing an odd number of fermions behaves overall as a fermion and has half-integer spin.
 
The fermionic or bosonic behaviour of composite systems is most evident when their constituents remain spatially separated. At shorter distances, the internal structure becomes important.
 
== Fermion pairing ==
Under certain conditions, fermions can pair together and collectively behave like bosons.
 
=== Superconductivity ===
In superconductors, electrons form [[Physics:Quantum Cooper pair|Cooper pairs]] through interactions mediated by phonons. These paired electrons can move collectively without electrical resistance.
 
=== Superfluidity ===
In helium-3, fermionic helium atoms pair through spin interactions and form a superfluid state at extremely low temperatures.
 
=== Composite fermions ==
Quasiparticles observed in the [[Physics:Quantum fractional quantum Hall effect|fractional quantum Hall effect]] are called composite fermions. They consist of electrons bound to quantized vortices.
 
== Physical interpretation ==
Fermions are responsible for the structure of matter because the Pauli exclusion principle prevents identical fermions from collapsing into the same state. This principle explains:
 
* atomic shell structure
* chemical behaviour
* stability of white dwarfs and neutron stars
* degeneracy pressure
* the organization of matter at microscopic scales


== Properties ==
== Physical consequences ==
Fermion statistics explain the periodic structure of atoms, electron degeneracy pressure, band filling in solids, and the stability of ordinary matter. In particle physics, fermion flavor, chirality, and mass mixing are central to weak interactions, neutrino oscillations, and matter-antimatter studies.<ref name="griffiths">{{cite book |last=Griffiths |first=David J. |title=Introduction to Elementary Particles |edition=2nd |publisher=Wiley-VCH |year=2008 |isbn=978-3-527-40601-2}}</ref>


* half-integer spin
* obey Fermi–Dirac statistics
* follow the Pauli exclusion principle
* include quarks and leptons
* form ordinary matter
* can combine into composite fermions
* may form paired bosonic states in superconductors and superfluids


=See also=
=See also=
{{#invoke:PhysicsQC|tocHeadingAndList|Physics:Quantum basics/See also/Matter}}
{{#invoke:PhysicsQC|tocHeadingAndList|Physics:Quantum basics/See also/Matter}}
== Notes ==
{{reflist|3}}


=References=
=References=

Revision as of 20:38, 19 May 2026


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A quantum fermion is a particle with half-integer spin that obeys Fermi-Dirac statistics. Fermions have antisymmetric many-particle wavefunctions, so identical fermions cannot occupy the same one-particle quantum state. This rule gives matter much of its structure, from atomic shells to degenerate stars.[1][2]

Complex yellow illustration of fermions with half-integer spin, excluded quantum states, and Pauli-structure cues.

Spin and statistics

The spin-statistics connection links half-integer spin with fermionic exchange behavior in relativistic quantum theory. Exchanging two identical fermions changes the sign of the many-body wavefunction. The resulting Pauli exclusion principle is not an ordinary force; it is a constraint on the allowed quantum states.[3]

Elementary and composite fermions

Elementary fermions include quarks and leptons. Composite systems can also behave as fermions when their total spin is half-integer, as in protons, neutrons, many nuclei, atoms, and quasiparticle excitations in condensed matter.

Physical consequences

Fermion statistics explain the periodic structure of atoms, electron degeneracy pressure, band filling in solids, and the stability of ordinary matter. In particle physics, fermion flavor, chirality, and mass mixing are central to weak interactions, neutrino oscillations, and matter-antimatter studies.[4]


See also

Table of contents (84 articles)

Index

Full contents

References

  1. ↑ Pauli, Wolfgang (1940). "The Connection Between Spin and Statistics". Physical Review 58 (8): 716-722. doi:10.1103/PhysRev.58.716. 
  2. ↑ Particle Data Group (2022). "Review of Particle Physics". Progress of Theoretical and Experimental Physics 2022 (8): 083C01. doi:10.1093/ptep/ptac097. 
  3. ↑ Peskin, Michael E.; Schroeder, Daniel V. (1995). An Introduction to Quantum Field Theory. Addison-Wesley. ISBN 978-0-201-50397-5. 
  4. ↑ Griffiths, David J. (2008). Introduction to Elementary Particles (2nd ed.). Wiley-VCH. ISBN 978-3-527-40601-2. 


Author: Harold Foppele


Source attribution: Fermion

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