particle physics, fermions are particles which obey Fermi-Dirac statistics; they are named after Enrico Fermi. In contrast to bosons, which have Bose-Einstein statistics, only one fermion can occupy a quantum stateat a given time; this is 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 associated with matterwhile bosons are often force carrierparticles, though the distinction between the two concepts is not clear cut in quantum physics.
Fermions can be elementary, like the
electron, or composite, like the proton. All observed fermions have half-integerspin, as opposed to bosons, which have integerspin. This is in accordance with the spin-statistics theoremwhich states that in any reasonable relativistic quantum field theory, particles with integer spin are bosons, while particles with half-integer spin are fermions.
Standard Modelthere are two types of elementary fermions: quarks and leptons. In total, there are 24 different fermions; 6 quarks and 6 leptons, each with a corresponding antiparticle:
quarks - 6 particles (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 6 corresponding antiparticles (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);
leptons - 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 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).
Composite fermions, such as
protons and neutrons, are essential building blocks of matter. Weakly interacting fermions can also display bosonic behaviour, as in superconductivity.
Definition and basic properties
By definition, fermions are particles which obey
Fermi-Dirac statistics: when one swaps two fermions, the wavefunctionof the system changes sign. [Srednicki (2007), pages 28-29] This " antisymmetricwavefunction" behavior implies that fermions are subject to the Pauli exclusion principle— no two fermions can occupy the same quantum stateat the same time. This results in "rigidity" or "stiffness" of states which include fermions (atomic nuclei, atoms, molecules, etc.), so fermions are sometimes said to be the constituents of matter, while bosons are said to be the particles that transmit interactions ( force carriers), or the constituents of radiation.The quantum fields of fermions are fermionic fields, obeying canonical anticommutation relations.
The Pauli exclusion principle for fermions and the associated rigidity of matter is responsible for the stability of the electron shells of atoms (thus for stability of atomic matter) and the complexity of atoms (making it impossible for all atomic electrons to occupy the same energy level), thus making complex
chemistrypossible. It is also responsible for the pressure within degenerate matterwhich largely governs the equilibrium state of white dwarfs and neutron stars. On a more everyday scale, the Pauli exclusion principle is a major contributor to the Young modulusof matter.
All known fermions are particles with half-integer spin: as an observer circles a fermion (or as the fermion rotates 360° about its axis) the
wavefunctionof the fermion changes sign. In the framework of nonrelativistic quantum mechanics, this is a purely empirical observation. However, in relativistic quantum field theory, the spin-statistics theoremshows that half-integer spin particles cannot be bosons and integer spin particles cannot be fermions. [Sakurai (1994), page 362]
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 particles are either fermions or bosons. The known elementary fermions are divided into two groups: quarks and leptons.
Quarksmake up protons, neutrons and other baryons, which are composite fermions; they also comprise mesons, which are composite bosons.
Leptons include the electronand similar, heavier particles (the muonand tauon); they also include neutrinos.
The known fermions of left-handed helicity experience
weak interactions while the known right-handed fermions do not. Or put another way, only left-handed fermions and right-handed anti-fermions interact with the W boson.
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-integerspin.
Examples include the following:
baryon, such as the protonor neutron, contains three fermionic quarks and is therefore a fermion;
*The nucleus of a
carbon-13atom contains 6 protons and 7 neutrons and is therefore a fermion;
helium-3(3He) is made of 2 protons, a neutron and 2 electrons 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.
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.
Fermions can exhibit bosonic behavior when they become loosely bound in pairs. This is the origin of
superconductivityand 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.
quantum field theory, there can be field configurations of bosons which are topologically twisted. These are coherent states (or solitons) which behave like a particle, and they can be fermionic even if all the elementary particles are bosons. This was discovered by Tony Skyrmein the early 1960s, so fermions made of bosons are named Skyrmions after him.
Skyrme's original example involves fields which take values on a three dimensional sphere, the original
nonlinear sigma modelthat describes the large distance behavior of pions. In Skyrme's model, which is reproduced in the large N or string approximation to QCD, the proton and neutron are fermionic topological solitons 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 smallest possible magnetic charge and a bosonic version of the electron would form a fermionic dyon.
*Sakurai, J.J. (1994). "Modern Quantum Mechanics" (Revised Edition), pp 361-363. Addison-Wesley Publishing Company, ISBN 0-201-53929-2.
*Srednicki, Mark (2007). " [http://www.physics.ucsb.edu/~mark/qft.html Quantum Field Theory] ", Cambridge University Press, ISBN 978-0521864497.
Wikimedia Foundation. 2010.