Spin–statistics theorem
Under the spin- statistics theorem of quantum physics refers to the theoretical justification for the empirical finding that all elementary particles with half-integer spin obey Fermi- Dirac statistics, ie so-called fermions, while all particles with integer spin of the Bose -Einstein statistics, i.e., so-called bosons.
Explanation of terms
Spin is the intrinsic angular momentum of the particles. A classic idea, somewhat like a small rotating body, is not possible here. All the particles are either integer (0, 1, 2, ... ), or half-integer (1/2, 3/2, 5/ 2, ...) spin, respectively, in units of the reduced Planck constant.
On the other hand, all particles are either Fermi -Dirac or Bose -Einstein statistics follow. These statistics describe the collective behavior of indistinguishable particles: only a single fermion ( Pauli principle ), but any number of bosons can be in a particular quantum state. In the formalism of quantum mechanics is the expressed thus, that the wave function of a group of indistinguishable fermions is anti-symmetric, that is, in exchange of the parameters of any two fermions changes its sign; however, the wave function of a group of indistinguishable bosons is symmetric, i.e., interchanging the parameters of any two bosons does not change its sign.
Examples of fermions are electrons, protons and neutrons, for bosons, the photon, 4He atoms and their nuclei, the alpha particles.
The Fermi-Dirac statistic provides, inter alia, the basis for the explanation of the Periodic Table of the Elements, the Bose -Einstein statistics of inter alia, the superfluid 4 He at low temperatures.
Discovery on the grounds
Although the spin and the two above-mentioned 1926 statistics were already known, only found Markus Fierz 1939 and 1940 Wolfgang Pauli theoretical justifications for the connection of phenomena. Both arguments were based on methods of relativistic quantum field theory, and it formed the view without (special ) theory of relativity can not be proved to the context. Pauli's proof has been generalized and refined in the following years.