| fermion | |
|---|---|
| Name | Fermion |
| Type | Elementary or composite particle |
| Statistics | Fermi–Dirac statistics |
| Spin | Half-integer (e.g. 1/2, 3/2) |
| Examples | Electron, Proton, Neutron, Quark, Neutrino |
fermion
A fermion is a particle that obeys the Fermi–Dirac statistics and the Pauli exclusion principle, characterized by half-integer spin. Fermions constitute the matter content of the universe and underpin the structure of atoms, nuclei, and electronic materials; their antisymmetric quantum states lead to the stability and diversity of chemical and solid-state systems. In Quantum physics and Quantum field theory, fermions contrast with bosons and play a central role in the Standard Model and many-body phenomena.
Fermions are defined by having half-integer intrinsic angular momentum (spin), such as 1/2, 3/2, etc., and by transforming under half-integer representations of the Lorentz group. The spin determines transformation properties under rotations and, via the spin–statistics theorem, enforces antisymmetric many-particle wavefunctions. Antisymmetry yields the Pauli exclusion principle, which forbids identical fermions from occupying the same quantum state and produces the degeneracy pressure responsible for the stability of white dwarfs and neutron stars. Fundamental conserved quantities associated with fermions include electric charge, baryon number, and lepton number in the context of the Standard Model.
Fermions are classified as either elementary or composite. Elementary fermions in the Standard Model include the six flavors of quarks and six flavors of leptons (charged leptons like the Electron and neutral leptons like the Neutrino), organized into three generations. Composite fermions arise from bound states of an odd number of fermionic constituents, e.g., baryons such as the Proton and Neutron (each composed of three quarks) and certain quasiparticles in solids. Extensions beyond the Standard Model propose additional fermions such as sterile neutrinos and supersymmetric partners like the sfermion (if supersymmetry is realized). Experimental classification relies on probes at facilities such as CERN, Fermilab, and national laboratories.
The formal connection between half-integer spin and antisymmetric exchange arises from the spin–statistics theorem proven in relativistic Quantum field theory under assumptions like locality and Lorentz invariance. For two identical fermions the multi-particle wavefunction changes sign upon particle exchange, Ψ(x1,x2) = −Ψ(x2,x1), which enforces antisymmetry. This property leads to observable consequences including exchange energy in atomic shells, the structure of the Periodic table, and the electrical and thermal properties of conductors and insulators governed by the Fermi surface. Mathematical frameworks that treat fermionic antisymmetry include second quantization with anticommutator algebra and Grassmann-valued path integrals used in quantum electrodynamics and lattice field theory simulations.
In the Standard Model, fermions are described by spinor fields: Dirac spinors for charged leptons and quarks, and Weyl spinors for chiral components. Interactions are mediated by gauge bosons of the gauge group SU(3)×SU(2)×U(1), with quarks participating in quantum chromodynamics (QCD) and leptons interacting via the electroweak force. Fermion masses arise through Yukawa couplings to the Higgs boson field and Higgs mechanism; neutrino masses require extensions such as the see-saw mechanism. Renormalization, anomaly cancellation (e.g., chiral anomaly considerations), and lattice QCD studies are central to understanding fermion dynamics at high energies; experiments at Large Hadron Collider and precision tests at SLAC National Accelerator Laboratory constrain fermion properties.
In condensed matter physics, emergent fermionic quasiparticles and many-body fermion behavior produce diverse phenomena. The notion of a Fermi liquid describes interacting fermions in metals (Landau theory), while non-Fermi-liquid behavior occurs in systems like high-temperature superconductors and heavy-fermion compounds studied at institutes such as the Max Planck Institute for Solid State Research. Composite excitations such as Cooper pairs are bosonic bound states of two electrons leading to superconductivity, whereas fractionalization in the fractional quantum Hall effect yields quasiparticles with fractional charge and anyonic statistics. Topological materials host exotic fermionic surface states (e.g., topological insulators) and Majorana fermions are predicted in certain superconducting heterostructures, with experimental efforts at universities and labs including Microsoft Station Q and various condensed-matter groups.
Key fermions observed and characterized include the Electron (discovered by J. J. Thomson), the Proton and Neutron (nuclear constituents studied by Rutherford and Chadwick), and the neutrino (postulated by Wolfgang Pauli and later detected by Clyde Cowan and Frederic Reines). High-energy collider experiments at CERN and Fermilab have produced and measured properties of heavy quarks like the top quark and bottom quark, while neutrino oscillation experiments (e.g., Super-Kamiokande, Sudbury Neutrino Observatory) probe neutrino mass and mixing. Precision atomic spectroscopy, scanning tunneling microscopy, and angle-resolved photoemission spectroscopy (ARPES) elucidate fermionic behavior in materials.
Fermions underpin technologies and phenomena reliant on quantum statistics: semiconductor electronics exploit electron band structure governed by the Fermi level; magnetic resonance and spintronics use electron and nuclear fermion spin; quantum computing platforms explore fermionic modes and Majorana zero modes for topological qubits. Astrophysical objects such as white dwarfs and neutron stars depend on fermionic degeneracy pressure, connecting microphysics to macroscopic astrophysical constraints measured by observatories including Chandra X-ray Observatory and gravitational-wave detectors. Research into engineered fermionic systems continues at universities and companies advancing quantum simulation and materials discovery.