The Scaling and Mass Expansion
- 82 Downloads
The scaling and mass expansion (shortly ‘sm-expansion’) is a new axiom for causal perturbation theory, which is a stronger version of a frequently used renormalization condition in terms of Steinmann’s scaling degree (Brunetti et al. in Commun Math Phys 208:623–661, 2000, Epstein et al. in Ann Inst Henri Poincaré 19A:211–295, 1973). If one quantizes the underlying free theory by using a Hadamard function (which is smooth in m ≥ 0), one can reduce renormalization of a massive model to the extension of a minimal set of mass-independent, almost homogeneously scaling distributions by a Taylor expansion in the mass m. The sm-expansion is a generalization of this Taylor expansion, which yields this crucial simplification of the renormalization of massive models also for the case that one quantizes with the Wightman two-point function, which contains a log(−(m 2(x 2 − ix 0 0))-term. We construct the general solution of the new system of axioms (i.e. the usual axioms of causal perturbation theory completed by the sm-expansion), and illustrate the method for a divergent diagram which contains a divergent subdiagram.
KeywordsDirect Extension Star Product Mass Expansion Renormalization Condition Commun Math Phys
Unable to display preview. Download preview PDF.
- 5.Dütsch, M., Fredenhagen, K., Keller, K.J., Rejzner, K.: Dimensional regularization in position space, and a forest formula for Epstein–Glaser renormalization. arXiv:1311.5424 [hep-th]
- 7.Dütsch, M.: Massive vector bosons: is the geometrical interpretation as a spontaneously broken gauge theory possible at all scales?. Work in preparationGoogle Scholar
- 14.Nikolov, N.M., Stora, R., Todorov, I.: Renormalization of massless Feynman amplitudes in configuration space. arXiv:1307.6854 [hep-th]
- 15.Steinmann, O.: Perturbation expansions in axiomatic field theory. In: Lecture Notes in Physics, vol. 11. Springer, Berlin (1971)Google Scholar
- 16.Stora, R.: Several unpublished notes. Among them: G. Popineau and R. Stora, A pedagogical remark on the main theorem of perturbative renormalization theory, LAPP–TH, Lyon, 1982; R. Stora, Differential algebras in Lagrangean field theory, Lectures at ETH, Zürich, 1993; etcGoogle Scholar