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%%% Owner: vip6
%%% Author(s): vip6, metalac
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\begin{document}
\begin{definition}
\emph{Fermions} are \htmladdnormallink{particles}{http://planetphysics.us/encyclopedia/Particle.html} with a half-integer \htmladdnormallink{spin}{http://planetphysics.us/encyclopedia/QuarkAntiquarkPair.html} value, and they are named after the famous Italian--American, Nobel Laureate physicist Enrico Fermi who built the first known operational \htmladdnormallink{nuclear reactor}{http://planetphysics.us/encyclopedia/Cyclotron.html} in Chicago as part of the Manhattan project during WWII. Several particles like \htmladdnormallink{leptons}{http://planetphysics.us/encyclopedia/Lepton.html}, \htmladdnormallink{quarks}{http://planetphysics.us/encyclopedia/ExtendedQuantumSymmetries.html} and \htmladdnormallink{baryons}{http://planetphysics.us/encyclopedia/QuarkAntiquarkPair.html} are all fermions.
\end{definition}
Since fermions have half-integer spin they obey a certain \htmladdnormallink{type}{http://planetphysics.us/encyclopedia/Bijective.html} of quantum-mechanical statistics called the {\em \htmladdnormallink{Fermi-Dirac statistics}{http://planetphysics.us/encyclopedia/FermiDiracDistribution.html}}, which also includes the consequences of the \htmladdnormallink{Pauli `exclusion principle';}{http://planetphysics.us/encyclopedia/PauliExclusionPrinciple.html} the latter principle states that no two fermions can occupy the same quantum mechanical state of a quantum mechanical \htmladdnormallink{system}{http://planetphysics.us/encyclopedia/SimilarityAndAnalogousSystemsDynamicAdjointnessAndTopologicalEquivalence.html}. The exclusion principle is the main reason that fermions are the building blocks of the existing physical world, and for the stability of the \htmladdnormallink{electron orbitals}{http://planetphysics.us/encyclopedia/MolecularOrbitals.html} in atoms and \htmladdnormallink{molecules}{http://planetphysics.us/encyclopedia/Molecule.html}.
All known `elementary particles': quarks, electrons, protons, etc are fermions with a spin value of 1/2-- and this suggests that the spin 1/2 elementary particle state is a unique, fundamental state of all stable matter in our \htmladdnormallink{physical Universe}{http://planetphysics.us/encyclopedia/MultiVerses.html}.
(One notes however that in superconducting systems that are usually macroscopically coherent quantum systems, the formation of phase-correlated `\htmladdnormallink{Cooper pairs}{http://planetphysics.us/encyclopedia/LongRangeCoupling.html}' of electrons coupled to the ionic lattice of the superconducting metal does apparently run counter to the Pauli exclusion principle; furthermore, the transition to \htmladdnormallink{superconductivity}{http://planetphysics.us/encyclopedia/WavePhenomena.html} involves necessarily a \htmladdnormallink{spontaneous symmetry breaking}{http://planetphysics.us/encyclopedia/LongRangeCoupling.html} that gives rise to \htmladdnormallink{Goldstone bosons}{http://planetphysics.us/encyclopedia/LongRangeCoupling.html} without which the superconductivity phenomenon/superconductivity phase transition would not be possible. Thus, in superconducting materials the electron pairs follow the \htmladdnormallink{Bose-Einstein statistics}{http://planetphysics.us/encyclopedia/BoseEinsteinStatistics.html} of very low-temperature condensates and behave like coupled \htmladdnormallink{boson}{http://planetphysics.us/encyclopedia/BoseEinsteinStatistics.html} chains, instead of the \htmladdnormallink{Fermi statistics}{http://planetphysics.us/encyclopedia/LongRangeCoupling.html} of uncorrelated electrons which is most common to high \htmladdnormallink{temperature}{http://planetphysics.us/encyclopedia/BoltzmannConstant.html} electrons; then, all such superconducting electron pairs are able to occupy the ground state with the lowest possible \htmladdnormallink{energy}{http://planetphysics.us/encyclopedia/CosmologicalConstant.html} in certain superconducting materials for temperatures below approximately 110 degree K.)
Fermions at high temperatures act on each other by exchanging \htmladdnormallink{field carrier}{http://planetphysics.us/encyclopedia/BoseEinsteinStatistics.html} bosons, just as, for example, in the case of quarks (that are fermions) and \htmladdnormallink{gluons}{http://planetphysics.us/encyclopedia/ExtendedQuantumSymmetries.html} (that are bosons) inside a \htmladdnormallink{nucleon}{http://planetphysics.us/encyclopedia/QuarkAntiquarkPair.html}, such as a proton or a \htmladdnormallink{neutron}{http://planetphysics.us/encyclopedia/Pions.html} of an atomic nucleus.
\end{document}
