Spin Statistics and Field Equations for any Spin

Abstract

In this article we prove spin statistics theorem for arbitrary massive (A, B) field in a representation theoretic manner. General Gamma matrices are introduced, and explicit forms for low spin are calculated. Spin sums and twisted spin sums are introduced to prove spin statistics and derive field equations respectively, and their relations are discussed. Klein Gordan equation is just the condition on the 4-momentum. Dirac equation (or massive Weyl equations) and Proca equation are shown to be examples of our general field equation.