Fermion
In particle physics, fermions are a group of elementary (or fundamental) particles that are the building blocks of matter. In the Standard Model, elementary particles are classified as fermions and bosons. Fermions are usually related with matter, whereas bosons are related with fundamental forces (or radiation).
Fermions are subdivided into quarks and leptons. Quarks are fermions that couple with a class of bosons known as gluons to form composite particles such as protons and neutrons. Leptons are those fermions that do not undergo coupling with gluons. Electrons are a well-known example of leptons.
Fermions come in pairs, and in three "generations." Everyday matter is composed of the first generation of fermions: two leptons, the electron and electron-neutrino; and two quarks, called Up and Down. Fermions obey what is known as "Fermi-Dirac statistics" and are named after Enrico Fermi.
Flavors of fermions
There are 24 fundamental types of fermions, referred to as fermionic "flavors." There are 12 quarks and 12 leptons, as listed below.
- 12 leptons - 6 particles and 6 corresponding antiparticles
Basic properties
All elementary particles are either fermions or bosons, depending on their spin.[1] According to this methodology, particles normally associated with matter are fermions, having half-integer spin. They are divided into the flavors noted above. Particles associated with fundamental forces are bosons, having integer spin.[2]
- In contrast to bosons, 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 (such as its spin) must be different from the rest.
Fermions have a half-integer spin. 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, which means 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 atomic nuclei, atoms, molecules, and so forth. For this reason, fermions are sometimes said to be the constituents of matter, and bosons to be particles that transmit interactions (forces), 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 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 dwarfs and neutron stars.
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 particles are either fermions or bosons. The known elementary fermions are divided into two groups: quarks and leptons.
The quarks make up protons and neutrons, which are composite fermions.
Leptons include the electron and similar, heavier particles (muon and tauon) and neutrino.
The known fermions of left-handed 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 bosons, nonrelativistic composite particles made up of more fundamental particles bound together through a potential energy are fermions or bosons, depending only on the number of fermions they contain:
- A composite particle containing an even number of fermions is a boson. Examples:
- A composite particle containing an odd number of fermions is a fermion. Examples:
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 Skyrmions 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 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.
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 (~10−10 m)—despite bosonic properties of the helium atoms. Thus, liquid helium has finite density comparable to the density of ordinary liquid matter.
Table of fermions and their properties
The following table is based in part on data gathered by the Particle Data Group.[3]
Generation 1 | |||||||
---|---|---|---|---|---|---|---|
Fermion (left-handed) |
Symbol | Electric charge |
Weak isospin |
Weak hypercharge |
Color charge * |
Mass ** | |
Electron | 511 keV | ||||||
Positron | 511 keV | ||||||
Electron-neutrino | < 2 eV **** | ||||||
Up quark | ~ 3 MeV *** | ||||||
Up antiquark | ~ 3 MeV *** | ||||||
Down quark | ~ 6 MeV *** | ||||||
Down antiquark | ~ 6 MeV *** | ||||||
Generation 2 | |||||||
Fermion (left-handed) |
Symbol | Electric charge |
Weak isospin |
Weak hypercharge |
Color charge * |
Mass ** | |
Muon | 106 MeV | ||||||
Antimuon | 106 MeV | ||||||
Muon-neutrino | < 2 eV **** | ||||||
Charm quark | ~ 1.337 GeV | ||||||
Charm antiquark | ~ 1.3 GeV | ||||||
Strange quark | ~ 100 MeV | ||||||
Strange antiquark | ~ 100 MeV | ||||||
Generation 3 | |||||||
Fermion (left-handed) |
Symbol | Electric charge |
Weak isospin |
Weak hypercharge |
Color charge * |
Mass ** | |
Tau lepton | 1.78 GeV | ||||||
Anti-tau lepton | 1.78 GeV | ||||||
Tau-neutrino | < 2 eV **** | ||||||
Top quark | 171 GeV | ||||||
Top antiquark | 171 GeV | ||||||
Bottom quark | ~ 4.2 GeV | ||||||
Bottom antiquark | ~ 4.2 GeV | ||||||
Notes:
|
See also
Notes
- ↑ The spin-statistics theorem identifies the resulting quantum statistics that differentiates fermions from bosons.
- ↑ Veltman, Martinus. 2003. Facts and Mysteries in Elementary Particle Physics. World Scientific. ISBN 981238149X.
- ↑ Quarks. Particle Data Group, Lawrence Berkeley Laboratory. Retrieved March 28, 2008.
- ↑ Particle Data Group: Neutrino mass, mixing, and flavor change (2006v)
ReferencesISBN links support NWE through referral fees
- Griffiths, David J. 1987. Introduction to Elementary Particles. New York: Wiley. ISBN 0471603864.
- Halzen, Francis, and Alan D. Martin. 1984. Quarks and Leptons: An Introductory Course in Modern Particle Physics. New York: Wiley. ISBN 0471887412.
- Povh, Bogdan. 1995. Particles and Nuclei: An Introduction to the Physical Concepts. Berlin: Springer-Verlag. ISBN 0387594396.
- Veltman, Martinus. 2003. Facts and Mysteries in Elementary Particle Physics. World Scientific. ISBN 981238149X.
External links
Particles in physics | |
---|---|
elementary particles | Elementary fermions: Quarks: u · d · s · c · b · t • Leptons: e · μ · τ · νe · νμ · ντ Elementary bosons: Gauge bosons: γ · g · W± · Z0 • Ghosts |
Composite particles | Hadrons: Baryons(list)/Hyperons/Nucleons: p · n · Δ · Λ · Σ · Ξ · Ω · Ξb • Mesons(list)/Quarkonia: π · K · ρ · J/ψ · Υ Other: Atomic nucleus • Atoms • Molecules • Positronium |
Hypothetical elementary particles | Superpartners: Axino · Dilatino · Chargino · Gluino · Gravitino · Higgsino · Neutralino · Sfermion · Slepton · Squark Other: Axion · Dilaton · Goldstone boson · Graviton · Higgs boson · Tachyon · X · Y · W' · Z' |
Hypothetical composite particles | Exotic hadrons: Exotic baryons: Pentaquark • Exotic mesons: Glueball · Tetraquark Other: Mesonic molecule |
Quasiparticles | Davydov soliton · Exciton · Magnon · Phonon · Plasmon · Polariton · Polaron |
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