fermionic

Fermionic describes particles or fields related to fermions, a class of particles with half-integer spin that obey the Pauli exclusion principle and Fermi-Dirac statistics. For identical fermions, the quantum state is antisymmetric under exchange, so swapping two particles multiplies the wavefunction by -1. This antisymmetry underlies many fundamental properties of matter.

The best-known fermions are electrons, protons, neutrons, quarks, and neutrinos. Leptons and quarks are fundamental fermions with spin 1/2. Protons and neutrons are composite fermions, made of three quarks. The exclusion principle shapes atomic structure and chemical behavior, preventing identical fermions from occupying the same quantum state and thereby influencing electronic configurations and spectra.

In quantum field theory, fermionic fields satisfy anticommutation relations. The Dirac equation describes spin-1/2 fermions, while Majorana fields describe neutral fermions that may be their own antiparticles. Creation and annihilation operators for fermions anticommute, enforcing the Pauli principle at the level of quantum states and particle excitations.

In condensed matter and many-body physics, systems of interacting fermions give rise to phenomena such as Fermi gases and Fermi liquids with a characteristic Fermi surface. Superconductivity and superfluidity often involve pairing of fermions into composite bosons (for example, Cooper pairs), allowing collective behavior that transcends the individual fermions. The term fermionic thus spans fundamental particles, their quantum fields, and emergent many-body phenomena.

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