Spin–statistics theorem
The spin–statistics theorem proves that the observed relationship between the intrinsic spin of a particle (angular momentum not due to the orbital motion) and the quantum particle statistics of collections of such particles is a consequence of the mathematics of quantum mechanics. According to the theorem, the many-body wave function for elementary particles with integer spin (bosons) is symmetric under the exchange of any two particles, whereas for particles with half-integer spin (fermions), the wave function is antisymmetric under such an exchange.