In particle physics, a fermion is a particle
that follows Fermi–Dirac statistics.
These particles obey the Pauli exclusion principle.
Fermions include all quarks and leptons, as
well as all composite particles made of an
odd number of these, such as all baryons and
many atoms and nuclei.
Fermions differ from bosons, which obey Bose–Einstein
statistics.
A fermion can be an elementary particle, such
as the electron, or it can be a composite
particle, such as the proton.
According to the spin-statistics theorem in
any reasonable relativistic quantum field
theory, particles with integer spin are bosons,
while particles with half-integer spin are
fermions.
In addition to the spin characteristic, fermions
have another specific property: they possess
conserved baryon or lepton quantum numbers.
Therefore, what is usually referred to as
the spin statistics relation is in fact a
spin statistics-quantum number relation.As
a consequence of the Pauli exclusion principle,
only one fermion can occupy a particular quantum
state at any given time.
If multiple fermions have the same spatial
probability distribution, then at least one
property of each fermion, such as its spin,
must be different.
Fermions are usually associated with matter,
whereas bosons are generally force carrier
particles, although in the current state of
particle physics the distinction between the
two concepts is unclear.
Weakly interacting fermions can also display
bosonic behavior under extreme conditions.
At low temperature fermions show superfluidity
for uncharged particles and superconductivity
for charged particles.
Composite fermions, such as protons and neutrons,
are the key building blocks of everyday matter.
The name fermion was coined by English theoretical
physicist Paul Dirac from the surname of Italian
physicist Enrico Fermi.
== Elementary fermions ==
The Standard Model recognizes two types of
elementary fermions: quarks and leptons.
In all, the model distinguishes 24 different
fermions.
There are six quarks (up, down, strange, charm,
bottom and top quarks), and six leptons (electron,
electron neutrino, muon, muon neutrino, tau
particle and tau neutrino), along with the
corresponding antiparticle of each of these.
Mathematically, fermions come in three types:
Weyl fermions (massless),
Dirac fermions (massive), and
Majorana fermions (each its own antiparticle).Most
Standard Model fermions are believed to be
Dirac fermions, although it is unknown at
this time whether the neutrinos are Dirac
or Majorana fermions (or both).
Dirac fermions can be treated as a combination
of two Weyl fermions.
In July 2015, Weyl fermions have been experimentally
realized in Weyl semimetals.
== Composite fermions ==
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-integer spin.
Examples include the following:
A baryon, such as the proton or neutron, contains
three fermionic quarks and thus it is a fermion.
The nucleus of a carbon-13 atom contains six
protons and seven neutrons and is therefore
a fermion.
The atom helium-3 (3He) is made of two protons,
one neutron, and two electrons, and therefore
it is 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) distances.
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 superconductivity and
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.
The quasiparticles of the fractional quantum
Hall effect are also known as composite fermions,
which are electrons with an even number of
quantized vortices attached to them.
=== Skyrmions ===
In a 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 constituent 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 involved fields
which take values on a three-dimensional sphere,
the original nonlinear sigma model which describes
the large distance behavior of pions.
In Skyrme's model, reproduced in the large
N or string approximation to quantum chromodynamics
(QCD), the proton and neutron are fermionic
topological solitons of the pion field.Whereas
Skyrme's example involved 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 will form a fermionic dyon.
The analogy between the Skyrme field and the
Higgs field of the electroweak sector has
been used to postulate that all fermions are
skyrmions.
This could explain why all known fermions
have baryon or lepton quantum numbers and
provide a physical mechanism for the Pauli
exclusion principle.
== See also ==
== 
Notes ==
