Fermion See Boson; Elementary Particles Any of a group of Subatomic Particles that have half-integral values of the quantum mechanical (see Quantum Theory) property called spin and are antisocial in that two of them cannot exist in the same quantum state. Fermions include the leptons and Quarks, which are the basic components of Matter. The Proton, Neutron, Electron, and Neutrinos are fermions. Fermi-Dirac statistics describe the behavior of systems of fermions.