Fermion
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[[Image:Standard Model of Elementary Particles.svg|thumb|300px|Standard Model of Elementary Particles]]
In [[particle physics]], '''fermions''' are particles with a ''[[half-integer]]'' [[Spin (physics)|spin]], such as [[proton]]s and [[electron]]s. They obey the [[Fermi-Dirac statistics]] and are named after [[Enrico Fermi]]. In the [[Standard Model]] there are two types of [[elementary particle|elementary]] fermions: [[quark|quarks]] and [[lepton|leptons]]. The 24 fundamental fermionic flavours are:
* 12 [[quark]]s - 6 [[Subatomic particle|particle]]s ({{SubatomicParticle|link=yes|Up quark}} · {{SubatomicParticle|link=yes|Down quark}} · {{SubatomicParticle|link=yes|Strange quark}} · {{SubatomicParticle|link=yes|Charm quark}} · {{SubatomicParticle|link=yes|Bottom quark}} · {{SubatomicParticle|link=yes|Top quark}}) with their 6 corresponding [[antiparticle]]s ({{SubatomicParticle|link=yes|Up antiquark}} · {{SubatomicParticle|link=yes|Down antiquark}} · {{SubatomicParticle|link=yes|Strange antiquark}} · {{SubatomicParticle|link=yes|Charm antiquark}} · {{SubatomicParticle|link=yes|Bottom antiquark}} · {{SubatomicParticle|link=yes|Top antiquark}});
* 12 [[lepton]]s - 6 particles ({{SubatomicParticle|link=yes|Electron}} · {{SubatomicParticle|link=yes|Muon}} · {{SubatomicParticle|link=yes|Tau}} · {{SubatomicParticle|link=yes|Electron neutrino}} · {{SubatomicParticle|link=yes|Muon Neutrino}} · {{SubatomicParticle|link=yes|Tau neutrino}}) with their 6 corresponding antiparticles ({{SubatomicParticle|link=yes|Positron}} · {{SubatomicParticle|link=yes|Antimuon}} · {{SubatomicParticle|link=yes|Antitauon}} · {{SubatomicParticle|link=yes|Electron antineutrino}} · {{SubatomicParticle|link=yes|Muon antineutrino}} · {{SubatomicParticle|link=yes|Tau antineutrino}}).
In contrast to [[boson]]s, only one fermion can occupy a [[quantum state]] at a given time (they obey the [[Pauli Exclusion Principle]]). Thus, if more than one fermion occupies the same place in space, the properties of each fermion (e.g. its spin) must be different from the rest. Therefore fermions are usually related with [[matter]] while [[boson]]s are related with [[radiation]], though the separation between the two is not clear in quantum physics.
==Basic properties==
Due to their half-integer spin, as an observer circles a fermion (or as the fermion rotates 360° about its axis) the [[wavefunction]] of the fermion changes sign. A related phenomenon is called an ''[[antisymmetric]] wavefunction'' behavior of a fermion. Fermions obey [[Fermi-Dirac statistics]], meaning that when one swaps two fermions, the [[wavefunction]] of the system changes sign. A consequence of this is the [[Pauli exclusion principle]] — no two fermions can occupy the same [[quantum state]] at the same time. This results in "rigidness" or "stiffness" of matter which include fermions (atomic nuclei, atoms, molecules, etc), so fermions are sometimes said to be the constituents of [[matter]], and [[bosons]] to be particles that transmit interactions ([[force]]s), or constituents of [[radiation]].
The [[Pauli exclusion principle]] obeyed by fermions is responsible for the "rigidness" of ordinary matter (it is a major contributor to [[Young modulus]]), and for the stability of the [[electron configuration|electron shells]] of atoms (thus for stability of atomic matter). It also is responsible for the complexity of atoms (making it impossible for all atomic electrons to occupy the same energy level), thus making complex [[chemistry]] possible. It is also responsible for the pressure within [[degenerate matter]] which largely governs the equilibrium state of [[white dwarf]]s and [[neutron star]]s.
In large systems, the difference between bosonic and fermionic statistics is only apparent at large densities when their wave functions overlap. At low densities, both types of statistics are well approximated by [[Maxwell-Boltzmann statistics]], which is described by [[classical mechanics]].
==Elementary fermions==
All observed [[elementary particle]]s are either fermions or [[boson|bosons]].
The known [[elementary particle|elementary]] fermions are divided into two groups: [[quark]]s and [[lepton]]s.
The [[quarks]] make up [[proton]]s and [[neutron]]s, which are composite fermions.
[[Lepton]]s include the [[electron]] and similar, heavier particles ([[muon]] and [[tauon]]) and [[neutrino|neutrino]].
The known fermions of left-handed [[helicity (particle physics)|helicity]] interact through the [[weak interaction]] while the known right-handed fermions do not. Or put another way, only left-handed fermions and right-handed anti-fermions couple to the [[W boson]].
==Composite fermions==
In addition to elementary fermions and [[boson|bosons]], nonrelativistic composite particles made up of more fundamental particles bound together through a potential energy are fermions or [[boson|bosons]], depending only on the number of fermions they contain:
* A composite particle containing an even number of fermions is a ''boson''. Examples:
**A [[meson]] contains two fermion [[quark|quarks]] and is a ''boson''.
**The [[atomic nucleus|nucleus]] of a [[carbon-12]] atom contains 6 protons and 6 neutrons (all fermions) and is also a ''boson''.
* A composite particle containing an odd number of fermions is a ''fermion''. Examples:
**A [[baryon]] contains three [[quark|quarks]] and is therefore a ''fermion''.
**The [[atomic nucleus|nucleus]] of a [[carbon-13]] atom contains 6 protons and 7 neutrons and is therefore a ''fermion''.
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.
In a [[quantum field theory]], the situation is more interesting. There can be field configurations of bosons which are topologically twisted. These are coherent states which behave like a particle, and they can be fermionic even if all the elementary particles are bosons. This was discovered by [[Tony Skyrme]] in the early 1960s, so fermions made of bosons are named [[Skyrmion]]s after him.
Skyrme's original example involves fields which take values on a three dimensional sphere, the original [[nonlinear sigma model]] that describes the large distance behavior of [[pion]]s. In Skyrme's model, which is reproduced in the [[1/N expansion|large N]] or [[AdS/QCD|string]] approximation to QCD, the proton and neutron are fermionic [[topological soliton]]s of the pion field. While Skyrme's example involves pion physics, there is a much more familiar example in quantum electrodynamics with a [[magnetic monopole]]. A bosonic monopole with the [[Dirac quantization condition|smallest possible magnetic charge]] and a bosonic version of the electron would form a fermionic [[dyon]].
Fermionic or bosonic behavior of a composite particle (or system) is only seen at large (compared to size of the system) distance. At proximity, where spatial structure begins to be important, a composite particle (or system) behaves according to its constituent makeup. For example, two atoms of [[helium]] can not share the same space if it is comparable by size to the size of the inner structure of the helium atom itself (~10<sup>−10</sup> m)—despite bosonic properties of the helium atoms. Thus, liquid helium has finite density comparable to the density of ordinary [[liquid]] matter.
== See also ==
* [[List of particles]]
* [[Fermionic field]]
* [[Identical particles]]
* [[Parastatistics]]
{{particles}}
[[Category:Particle physics]]
[[Category:Quantum field theory]]
[[Category:Subatomic particles]]
[[Category:Fermions|*]]
[[Category:Fundamental physics concepts]]
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