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
