In particle physics, a fermion is any particle characterized by Fermi–Dirac
statistics. These particles obey the Pauli exclusion principle. Fermions
include all quarks and leptons, as well as any composite particle 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.
Besides this spin characteristic, fermions have another specific property:
they possess conserved baryon or lepton quantum numbers. Therefore what is
usually referred 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. 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. Weakly interacting fermions can also
display bosonic behavior under extreme conditions, such as superconductivity.
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, and six leptons, along with the
corresponding antiparticle of each of these.
Mathematically, fermions come in three types - Weyl fermions, Dirac fermions,
and Majorana fermions. 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. Dirac fermions can be treated as a combination of two Weyl
fermions. So far there is no known example of Weyl fermion in particle
physics. In July 2015, Weyl fermions have been experimentally realized in
Weyl semimetals. Composite fermions
Composite particles 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 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 is only seen at large distances. At proximity, where spatial
structure begins to be important, a composite particle 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 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, 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