In particle physics, a fermion (named after Enrico Fermi) is any particle which obeys the Fermi–Dirac statistics (and follows the Pauli exclusion principle). Fermions contrast with 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. The spin-statistics theorem holds that, in any reasonable relativistic quantum field theory, particles with integer spin are bosons, while particles with half-integer spin are fermions.
In contrast to bosons, only one fermion can occupy a particular quantum state at any given time. If more than one fermion occupies the same physical space, 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 quantum physics the distinction between the two concepts is unclear.
The Standard Model recognizes two types of elementary fermions: quarks and leptons. In all, the model distinguishes 24 different fermions: 6 quarks and 6 leptons, each with a corresponding anti-particle.
Composite fermions, such as protons and neutrons, are key building blocks of matter. Weakly interacting fermions can also display bosonic behavior under extreme conditions, such as in superconductivity.
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By definition, fermions are particles which obey Fermi–Dirac statistics: when one swaps two fermions, the wavefunction of the system changes sign.[1] This "antisymmetric wavefunction" behavior implies that fermions are subject to the Pauli exclusion principle, i.e. no two fermions can occupy the same quantum state at the same time. This results in "rigidity" or "stiffness" of states that include fermions (atomic nuclei, atoms, molecules, etc.), so fermions are sometimes said to be the constituents of matter, while bosons are said to be the particles that transmit interactions (i.e. force carriers) or the constituents of electromagnetic radiation.
The quantum fields of fermions are fermionic fields, obeying canonical anticommutation relations.
The Pauli exclusion principle for fermions and the associated rigidity of matter is responsible for the stability of the electron shells of atoms (thus for the stability of atomic matter), and 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. On a more everyday scale, the Pauli exclusion principle is a major contributor to the Young's modulus of elastic material.
All known fermions are particles with 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. In the framework of non-relativistic quantum mechanics, this is a purely empirical observation. However, in relativistic quantum field theory, the spin-statistics theorem shows that half-integer spin particles cannot be bosons and integer spin particles cannot be fermions.[2]
In large systems, the difference between bosonic and fermionic statistics is only apparent at large densities, when their wavefunctions overlap. At low densities, both types of statistics are well approximated by Maxwell-Boltzmann statistics, which is described by classical mechanics.
Another specific property of fermions, besides the Pauli exclusion principle is that all known fermions have baryon or lepton quantum numbers. So far no elementary bosons with non-vanishing lepton (baryon) quantum numbers have been observed.
The Standard Model distinguishes two types of elementary fermions: quarks and leptons. In total, 24 different fermions are recognized, 6 quarks and 6 leptons, each with a corresponding antiparticle:
All observed elementary particles are either fermions or bosons. The known elementary fermions are divided into two groups: quarks and leptons.
All known fermions with left-handed helicity (spin) experience weak interactions, whereas all known right-handed fermions do not. In other words, only left-handed fermions and right-handed antifermions interact with the W boson.
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:
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.
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 [3] 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.
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