1.Departamento de Física,Universidade Federal de Juiz de Fora,Juiz de Fora,Brazil;2.Escuela de Matemática,Universidad de Costa Rica,San José,Costa Rica
Abstract:
For a renormalizability proof of perturbative models in the Epstein–Glaser scheme with string-localized quantum fields, one needs to know what freedom one has in the definition of time-ordered products of the interaction Lagrangian. This paper provides a first step in that direction. The basic issue is the presence of an open set of n-tuples of strings which cannot be chronologically ordered. We resolve it by showing that almost all such string configurations can be dissected into finitely many pieces which can indeed be chronologically ordered. This fixes the time-ordered products of linear field factors outside a nullset of string configurations. (The extension across the nullset, as well as the definition of time-ordered products of Wick monomials, will be discussed elsewhere).