The cluster-property of the \(S\)-matrix (Q2723271)

The aim of this thesis is to give a mathematically rigorous derivation of the cluster property of the \(S\)-matrix in quantum field theory which was proposed originally by \textit{E. H. Wichmann} and \textit{J. H. Grichton} [J. Phys. Rev. 132, No. 6, 2788--2799 (1963)]. To that end the direct use of the creation- and destruction-operators is omitted in the continuous spectrum and replaced by operator valued integral kernels. In the first chapter the irreducible representations of the Poincaré group for free particles, and the construction of the respective Fock spaces is considered. In Chapter 2 the cluster property is defined, and a criterion for the \(S\)-operator to process this property is given. Chapter 3 is concerned with the Fourier transforms and explains how the usual interpretation with creation- and annihilation operators fits into the mathematically rigorous formalism. In Chapter 5 the criterion for the cluster property to hold true is formulated for the integral kernels. Several functional analytic considerations, and the introduction of a concept of connected integral kernels in Chapters 7 through 8 lead to a necessary and sufficient condition for the cluster property of the \(S\)-operator of connected components. -- This work is very readable and instructive.