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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

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.

Received:
Jan 14, 2014
Published:
Jan 14, 2014
Keywords:
Perturbative quantum field theory, Causal perturbation theory

Related publications

inJournal
2015 Repository Open Access
Michael Dütsch

The scaling and mass expansion

In: Annales Henri Poincaré, 16 (2015) 1, pp. 163-188