# Fermion

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In particle physics, fermions are particles that obey Fermi–Dirac statistics. They are named after Enrico Fermi. In contrast to bosons, which obey Bose–Einstein statistics, only one fermion can occupy a quantum state at a given time.

If more than one fermion occupies the same place in space, at least one other property for each fermion, e.g., its spin, must be different from the rest. Fermions are usually associated with matter while bosons are often force carrier particles, though the distinction between the two concepts in quantum physics is unclear.

A fermion can be an elementary particle, like the electron, or a composite particle, like the proton. The spin-statistics theorem states that in any reasonable relativistic quantum field theory particles with integer spin are bosons, while particles with half-integer spin are fermions.

The Standard Model recognizes two types of elementary fermions: quarks and leptons. In total, the model distinguishes 24 different fermions: 6 quarks and 6 leptons, each with a corresponding antiparticle.

Composite fermions, such as protons and neutrons, are essential building blocks of matter. Weakly interacting fermions can also display bosonic behavior, as in superconductivity.

## Contents

### Definition and basic properties

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 — no two fermions can occupy the same quantum state at the same time. This results in "rigidity" or "stiffness" of states which 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 (force carriers), or the constituents of radiation. The quantum fields of fermions are fermionic fields, obeying canonical anticommutation relations.