# Dictionary Definition

fermion n : any particle that obeys Fermi-Dirac
statistics and is subject to the Pauli exclusion principle

# User Contributed Dictionary

### Pronunciation

/ˈfɜːmɪɒn/### Noun

#### Translations

#### Derived terms

# Extensive Definition

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 ( · · · · · ) with their 6 corresponding antiparticles ( · · · · · );

- 12 leptons - 6 particles ( · · · · · ) with their 6 corresponding antiparticles ( · · · · · ).

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 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:

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.

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