Cluster Decomposition and the Spin-Statistics Theorem inS-Matrix Theory

Abstract

This paper establishes within $S$-matrix theory the connection between spin and statistics; namely, that the multiparticle-state vectors are symmetric or antisymmetric for permutation of identical particles according as the particle concerned has integral or half-integral spin. The proof given, which is simpler than previous $S$-matrix proofs, depends on the cluster-decomposition property, crossing symmetry, and Hermitian analyticity. A considerable part of the paper is concerned with establishing a suitable framework to formulate the first of these properties, cluster decomposition. To this end we develop from first principles the idea of the tensor product $f\ensuremath{\bigotimes}g$ which, for any two state vectors $f$ and $g$, represents the composite state ($f$ and $g$).