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 Poincar, 19A:211-295, 1973). If one quantizes the underlying free theory by using a Hadamard function (which is smooth in m a parts per thousand yen 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.
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机译：缩放和质量扩展（简称“ sm扩展”）是因果微扰理论的新公理，它是根据Steinmann缩放比例度（Brunetti等人，Commun Math Phys 208： 623-661，2000，Epstein等人，Ann Inst Henri Poincar，19A：211-295，1973）。如果使用Hadamard函数（在千分之一的日元中为0的平滑分量）对基本的自由理论进行量化，则可以将大规模模型的重新归一化减少为最小的与质量无关的，几乎均匀缩放的分布集的扩展。质量的泰勒展开式sm展开式是此泰勒展开式的推广，对于使用怀特曼两点函数进行量化的情况（包含log（-（m（2）（ x（2）-ix（0）0））项，我们构造了新的公理系统（即由因数展开式完成的因果扰动理论的通常公理）的一般解，并举例说明了发散的方法该图包含发散的子图。
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