Preprint 4/2014
The scaling and mass expansion
Michael Dütsch
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Submission date: 14. Jan. 2014
Pages: 22
published in: Annales Henri Poincaré, 16 (2015) 1, p. 163-188 
DOI number (of the published article): 10.1007/s00023-014-0324-6
Bibtex
Keywords and phrases: Perturbative quantum field theory, Causal perturbation theory
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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 ≥ 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(−(m2(x2 −ix00))-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.