Fermion

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File:Standard Model of Elementary Particles.svg
Standard Model of Elementary Particles.

In particle physics, fermions are particles with a half-integer spin, such as protons and electrons. They obey the Fermi-Dirac statistics and are named after Enrico Fermi. In the Standard Model there are two types of elementary fermions: quarks and leptons. The 24 fundamental fermionic flavours are:

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 (e.g. its spin) must be different from the rest. Therefore fermions are usually related with matter while bosons are related with radiation, though the separation between the two is not clear in quantum physics.

Overview of elementary particles

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 twelve flavors. Particles associated with fundamental forces are bosons, having integer spin.[2]

Quarks — up, down, charm, strange, top, bottom
Leptons — electron neutrino, electron, muon neutrino, muon, tau neutrino, tau
Gauge bosons — gluon, W and Z bosons, photon
Other bosons — Higgs boson, graviton

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 (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 meson contains two fermion quarks and is a boson.
    • The 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 quarks and is therefore a fermion.
    • The 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 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.

List of standard model fermions

This table is based in part on data gathered by the Particle Data Group.[3]

Left-handed fermions in the Standard Model
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:
  • * These are not ordinary abelian charges, which can be added together, but are labels of group representations of Lie groups.
  • ** Mass is really a coupling between a left-handed fermion and a right-handed fermion. For example, the mass of an electron is really a coupling between a left-handed electron and a right-handed electron, which is the antiparticle of a left-handed positron. Also neutrinos show large mixings in their mass coupling, so it's not accurate to talk about neutrino masses in the flavor basis or to suggest a left-handed electron antineutrino.
  • *** The masses of baryons and hadrons and various cross-sections are the experimentally measured quantities. Since quarks can't be isolated because of QCD confinement, the quantity here is supposed to be the mass of the quark at the renormalization scale of the QCD scale.
  • **** The Standard Model assumes that neutrinos are massless. However, several contemporary experiments prove that neutrinos oscillate between their flavor states, which could not happen if all were massless.[4] It is straightforward to extend the model to fit these data, but there are many possibilities, so the mass eigenstates are still open. (See Neutrino.)

See also

Notes

  1. The spin-statistics theorem identifies the resulting quantum statistics that differentiates fermions from bosons.
  2. Veltman, Martinus. 2003. Facts and Mysteries in Elementary Particle Physics. World Scientific. ISBN 981238149X.
  3. Quarks. Lawrence Berkeley Laboratory. Retrieved March 28, 2008.
  4. Particle Data Group: Neutrino mass, mixing, and flavor change (2006v)

References
ISBN 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

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