Place of Hilbert Space inS-Matrix Theory

Abstract

Properties of the $S$ matrix usually regarded as essential to an analytic $S$-matrix theory are shown to be sufficient for the construction of a Hilbert space of asymptotic states and a unitary $S$ operator which maps this space onto itself. This means that, contrary to what one might expect, a formulation of $S$-matrix theory which makes no explicit reference to Hilbert space is in no sense more general than a more conventional formulation in terms of Hilbert space.