# The scaling and mass expansion

January 08, 2014

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.

Keywords:

*none*