On the Connection between Spin and Statistics

In the following paper we conclude for the relativistically invariant wave equation for free particles: From postulate (I), according to which the energy must be positive, the necessity of Fermi-Dirac statistics for particles with arbitrary half-integral spin; from postulate (II), according to which observables on different space-time points with a space-like distance are commutable, the necessity of Einstein-Bose statistics for particles with arbitrary integral spin. It has been found useful to djvide the quantities which are irreducible against Lorentz transformations into four symmetry classes which have a commutable multiplication like +1, —1, +e, —e with c =1.