# String chopping and time-ordered products of linear string-localized quantum fields

September 11, 2017

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.)

Keywords:

*none*