 98603 S. Albeverio (albeverio@unibonn.de),, H. Gottschalk (hanno.gottschalk@ruhrunibochum.de),, J.L. Wu (jianglun.wu@ruhrunibochum.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
nonGaussian 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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