Fermion

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:

• 12 quarks - 6 particles (u · d · s · c · b · t) with their 6 corresponding antiparticles (u · d · s · c · b · t);

• 12 leptons - 6 particles (e⁻ · μ⁻ · τ⁻ · νe · νμ · ντ) with their 6 corresponding antiparticles (e⁺ · μ⁺ · τ⁺ · νe · νμ · ντ).

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.

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.

See also

• Boson
• Fundamental particle
• Lepton
• Particle physics

References

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