Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.
MiS Preprint
4/2014
The scaling and mass expansion
Michael Dütsch
Abstract
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.
If one quantizes the underlying free theory by using a Hadamard function (which is smooth in $m\geq 0$), 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.
