POLYNOMIAL BEHABIOUR OF SCATTERING AMPLITUDES AT FIXED MOMENTUM TRANSFER IN THEORIES WITH LOCAL OBSERVABLES

It is shown that, in theories of exactly localized observables, of the type proposed by Araki and Haag, the reaction amplitude for two particles giving two particles is polynomially bounded in s for fixed momentum transfer t<0. The proof does not need observables localized in space-time regions of arbitrarily small volume, but uses relativistic invariance in an essential way. It is given for the case of spinless neutral particles, but is easily extendable to all cases of charge and spin. The proof can also be generalized to the case of particles described by regularized products {Mathematical expression} of Wightman or Jaffe fields. © 1969 Springer-Verlag.