In particle physics, a fermion (a name coined by Paul Dirac from the surname of Enrico Fermi) is any particle characterized by Fermi–Dirac statistics and following 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 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 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.

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.

Read more about Fermion:  Composite Fermions

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Helicity Basis - Fermion (spin 1/2) Wavefunction
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Staggered Fermion
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Numerical Sign Problem - The Sign Problem in Field Theory
... In a field theory approach to multi-particle systems, the fermion density is controlled by the value of the fermion chemical potential ... The sum over fermion fields can be performed analytically, and one is left with a sum over the bosonic fields (which may have been originally part of the theory, or have been produced by a Hubbard-Strato ... This typically occurs in theories of fermions when the fermion chemical potential is nonzero, i.e ...
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