Piecewise analyticity ofS-matrix elements and nonlocal interactions

Abstract

In local quantum field theories ultraviolet divergences may be avoided by admitting an indefinite metric in the quantum-mechanical state space. The occurrence of negative-norm and zero-norm states (ghost states) in general leads to a violation of the unitarity of the physicalS-matrix. In order to unitarize the theory in the physical subspace an appropriate procedure has to be employed which leads to the suppression of unphysical channels and as a consequence produces nonanalytic points at the thresholds of these channels which destroy the global analyticity of theS-matrix in thes-plane. If these nonanalytic points occur in the physical region they simulate nonlocal interactions which decrease with a certain power of the distance. The nonlocal effects are strongest if anS-wave 2-particle ghost channel is suppressed and are less aggravating if they involve ghost channels with higher angular momentum and a larger number of particles.