Cluster Decomposition and the Spin-Statistics Theorem in S-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⊗g which, for any two state vectors f and g, represents the composite state (f and g).
- Publication:
-
Physical Review
- Pub Date:
- January 1967
- DOI:
- 10.1103/PhysRev.153.1636
- Bibcode:
- 1967PhRv..153.1636F