Derivation of theCPTTheorem and the Connection between Spin and Statistics from Postulates of theS-Matrix Theory

The $\mathrm{CPT}$ theorem and the normal connection between spin and statistics are shown to be consequences of postulates of the $S$-matrix approach to elementary particle physics. The postulates are much weaker than those of field theory. Neither local fields nor any reference to space-time points are used. Quantum commutation relations and properties of the vacuum play no role. Completeness of the asymptotic states and positive definiteness of the metric are not required, though certain weaker asymptotic conditions prevail. The proofs depend on unitarity, macroscopic relativistic invariance, and a very weak analyticity requirement on the mass-shell scattering functions. The proofs are in the framework of the new $S$-matrix approach to elementary particle physics, which is established on a formal basis.