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 Stochastic partial differential equations and applications, Proc. Trento Conference on Stochastic Analysis, Trento 2000, eds. G. Da Prato, L. Tubaro, M. Dekker 2002 · 16 pages
arxiv created 2004/09/14 · arxiv updated 2009/12/01
In this article we review the construction of local, relativistic quantum vector fields by analytic continuation of Euclidean vector fields obtained as solutions of covariant SPDEs. We revise the formulation of such SPDEs by introducing new Gaussian noise terms -- a procedure which avoids the re-definition of the two point functions needed in previous approaches in order to obtain relativistic fields with nontrivial scattering. We describe the construction of asymptotic states and the scattering of the analytically continued solutions of these new SPDEs and we give precise conditions for nontrivial and well-defined scattering.