1 Fermions
Definition 1.1.
Fermions are particles with a half-integer spin value, and they are named after the
famous Italian–American, Nobel Laureate physicist Enrico Fermi who built the first known
operational nuclear reactor in Chicago as part of the Manhattan project during WWII.
Several particles like leptons, quarks and baryons are all fermions.
Since fermions have half-integer spin they obey a certain type of quantum-mechanical statistics
called the Fermi-Dirac statistics, which also includes the consequences of the Pauli ‘exclusion
principle’; the latter principle states that no two fermions can occupy the same quantum
mechanical state of a quantum mechanical system. The exclusion principle is the main reason that
fermions are the building blocks of the existing physical world, and for the stability of the electron
orbitals in atoms and molecules.
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 physical Universe.
(One notes however that in superconducting systems that are usually macroscopically coherent
quantum systems, the formation of phase-correlated ‘Cooper pairs’ of electrons coupled to the ionic
lattice of the superconducting metal does apparently run counter to the Pauli exclusion principle;
furthermore, the transition to superconductivity involves necessarily a spontaneous
symmetry breaking that gives rise to Goldstone bosons without which the superconductivity
phenomenon/superconductivity phase transition would not be possible. Thus, in superconducting
materials the electron pairs follow the Bose-Einstein statistics of very low-temperature condensates
and behave like coupled boson chains, instead of the Fermi statistics of uncorrelated electrons
which is most common to high temperature electrons; then, all such superconducting
electron pairs are able to occupy the ground state with the lowest possible energy in
certain superconducting materials for temperatures below approximately 110 degree
K.)
Fermions at high temperatures act on each other by exchanging field carrier bosons, just as, for
example, in the case of quarks (that are fermions) and gluons (that are bosons) inside a nucleon,
such as a proton or a neutron of an atomic nucleus.
