| Fermion | |
|---|---|
| Name | Fermion |
| Type | Elementary particle |
| Composition | Elementary or composite |
| Statistics | Fermi–Dirac statistics |
| Spin | Half-integer |
| Discovered | 1926 (Fermi–Dirac), concept developed through 20th century |
Fermion
Fermions are particles that obey Fermi–Dirac statistics and have half-integer intrinsic spin, making them the basic constituents of ordinary matter in Quantum physics. They include both fundamental particles such as electrons and quarks and composite particles such as protons and neutrons; their behavior underlies the structure of atoms, solids, and nuclear matter. Understanding fermions is central to particle physics and to technologies derived from condensed matter physics.
In quantum theory a fermion is defined by its transformation properties under rotations and the permutation of identical particles: fermions carry half-integer spin (e.g., 1/2, 3/2) and their multi-particle wavefunctions are antisymmetric under exchange, a property encoded by the sign change of the wavefunction under particle interchange. This antisymmetry is the hallmark of Fermi–Dirac statistics, formulated by Enrico Fermi and Paul Dirac in the 1920s, and contrasted with Bose–Einstein statistics for bosons such as the photon. In relativistic formulations fermions are described by spinor fields satisfying the Dirac equation or, for neutral Majorana fermions, the Majorana equation. Key mathematical tools include spinors, Grassmann numbers in path integrals, and representations of the Lorentz group and Poincaré group.
The half-integer spin of fermions implies the Pauli exclusion principle, first articulated by Wolfgang Pauli in 1925, which prevents identical fermions from occupying the same quantum state. This principle explains the structure of periodic table and chemical behavior via electron configuration in atoms studied by Niels Bohr and later quantum chemists. In many-body systems the exclusion principle leads to the formation of a Fermi surface in metals and governs degeneracy pressure in dense astrophysical objects like white dwarfs and neutron stars; the latter are modeled using nuclear physics and neutron star equations of state from collaborations at institutions like CERN and Brookhaven National Laboratory.
The Standard Model classifies fundamental fermions into three generations of leptons and quarks. Leptons include the electron, muon, tau, and their associated neutrinos (e.g., electron neutrino). Quarks combine via the strong interaction described by quantum chromodynamics to form composite fermions called hadrons: baryons (e.g., proton, neutron) are fermionic composites of three quarks; mesons are bosonic composites. Beyond Standard Model proposals posit additional fermions such as sterile neutrinos, supersymmetric partners like the neutralino (a fermionic sparticle), or exotic fermions in Grand Unified Theory models. Experimental programs at Fermilab, KEK, and CERN have been central to discovering and constraining fermion properties.
In quantum field theory fermions are quantized using anticommuting field operators to enforce the exclusion principle and Pauli statistics; canonical quantization yields creation and annihilation operators with anticommutation relations. The Dirac field couples to gauge fields of the electroweak interaction and quantum electrodynamics via terms in the Lagrangian, producing phenomena such as anomalous magnetic moment corrections measured for the electron and muon in precision experiments at Harvard University and Brookhaven National Laboratory. Chiral symmetry breaking, Yukawa couplings in the Higgs mechanism, and fermion mass generation are central problems tied to flavor physics and searches performed by collaborations like ATLAS and CMS at the Large Hadron Collider.
In condensed matter physics emergent fermionic quasiparticles explain electronic conduction, magnetism, and superconductivity. Electrons in solids form a Fermi sea and excitations near the Fermi surface are described by Landau Fermi liquid theory; departures produce non-Fermi liquids studied at Bell Labs and in modern materials research. Composite fermions arise in the fractional quantum Hall effect research pioneered by Robert B. Laughlin and at facilities like MIT and Princeton University. Unconventional fermionic excitations, including Majorana fermions as quasiparticles in topological superconductors and Dirac fermions in graphene, have motivated device proposals for quantum computing pursued by companies such as Microsoft and research groups at Caltech. Fermionic statistics also shape BCS superconductivity where paired fermions form bosonic Cooper pairs.
Fermions are observed directly in particle detectors and indirectly via scattering, decay signatures, and spectroscopy. Accelerator experiments at SLAC National Accelerator Laboratory, CERN, and Fermilab have produced leptons and quarks whose properties are reconstructed using tracking detectors, calorimeters, and particle identification systems. Neutrino observatories like Super-Kamiokande and IceCube detect fermionic neutrino interactions; beta decay and neutrino oscillation experiments such as SNO and Daya Bay Reactor Neutrino Experiment probe neutrino masses and mixing. Precision atomic measurements of the electron g-factor at University of Washington and measurements of hadron structure at Jefferson Lab constrain theory. Searches for rare fermionic processes and for hypothetical fermions (e.g., heavy neutral leptons) continue at fixed-target experiments and collider upgrades supported by international collaborations.
Category:Particle physics Category:Quantum mechanics Category:Condensed matter physics