2004/09/14 by S. Albeverio, H. Gottschalk, J. -L. Wu
Physics and Astronomy · Mathematics · #math-ph #math.MP #msc:81T10 #msc:81T05
published as Rept.Math.Phys. 40 (1997) 385-394
arxiv created 2004/09/14 · arxiv updated 2009/12/01
We discuss Euclidean covariant vector random fields as the solution of stochastic partial differential equations of the form DA=η, where D is a covariant (w.r.t. a representation τof SO(d)) differential operator with "positive mass spectrum" and η 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 Lugewicz. Based on these formulae we give necessary and sufficient conditions on the mass spectrum of D which imply nontrivial scattering behaviour of relativistic quantum vector fields associated to the given sequence of Wightman functions. We compute the scattering amplitudes explicitly and we find that the masses of particles in the obtained theory are determined by the mass spectrum of D.