String Chopping and Time-ordered Products of Linear String-localized Quantum Fields
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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).
KeywordsRelativistic quantum field theory Locality Epstein-Glaser perturbative construction Time-ordered products
Mathematics Subject Classification (2010)81T15 81T05
This research was generously supported by the program “Research in Pairs” of the Mathematisches Forschungsinstitut at Oberwolfach in November 2015. JM and JCV are grateful to José M. Gracia-Bondía for helpful discussions, at Oberwolfach and later. We thank the referee for pertinent comments, which helped to fine-tune the paper. JM and LC have received financial support by the Brasilian research agencies CNPq and CAPES, respectively. They are also grateful to Finep. The project has received funding from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No. 690575. JCV acknowledges support from the Vicerrectoría de Investigación of the Universidad de Costa Rica.
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