98-603 S. Albeverio (albeverio@uni-bonn.de),, H. Gottschalk (hanno.gottschalk@ruhr-uni-bochum.de),, J.-L. Wu (jiang-lun.wu@ruhr-uni-bochum.de)

Scattering behaviour of quantum vector fields obtained from Euclidean covariant SPDEs (134K, LATeX 2e) Sep 14, 98

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Abstract. We discuss Euclidean covariant vector random fields as the solution of stochastic partial differential equations of the form $DA=\eta$, where $D$ is a covariant (w.r.t. a representation $\tau$ of $SO(d)$) differential operator with "positive mass spectrum" and $\eta$ is a non-Gaussian white noise. We obtain explicit formulae for the Fourier transformed truncated Wightman functions, using the analytic continuation of Schwinger functions discussed by Becker, Gielerak and {\L}ugewicz. Based on these formulae we give necessary and sufficient conditions on the mass spectrum of $D$ which imply nontrival scattering behaviour of relativistic quantum vector fileds associated to the given sequence of Wightman functions. We compute the scattering amplitudes explicitly and we find the masses of particles in the obtained theroy are determined by the mass spectrum of $D$.

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