The connection between spin and statistics

Abstract

After some brief historical remarks we recall the first demonstration of the Spin-Statistics theorem by Pauli, and some further developments, like Streater-Wightman's, in the axiomatic considerations. Sudarshan's short proof then follows by considering only the time part of the kinetic term in the lagrangian: the identity SU(2)=Sp(1,C) is crucial for the argument. Possible generalization to arbitrary dimensions are explored, and seen to depend crucially on the type of spinors, obeying Bott's periodicity 8. In particular, it turns out that for space dimentions (7, 8, or 9) modulo 8, the conventional result does not automatically hold: there can be no Fermions in these dimensions.