标度代数与点状场：重整化的非微扰方法
Scaling algebras and pointlike fields: A nonperturbative approach to renormalization
摘要：
我们提出了一种在量子场论中进行短程分析的方法，这种方法不需要事先选择重整化处方。我们从一个具有相关点状量子场的局部代数网出发。网有一个自然定义的缩放限制的意义上的Buchholz和Verch，我们调查的效果，这一限制的点状领域。对于域和它们的算子乘积展开，可以建立一个定义明确的极限过程。这总是可以用通常意义上的乘法重整化来解释，其中重整化因子由我们的分析确定。我们还考虑了对称作用的极限。特别地，对于合适的极限状态，标度变换组在极限理论中引起膨胀对称性。
英文摘要：
We present a method of short-distance analysis in quantum field theory that does not require choosing a renormalization prescription a priori. We set out from a local net of algebras with associated pointlike quantum fields. The net has a naturally defined scaling limit in the sense of Buchholz and Verch; we investigate the effect of this limit on the pointlike fields. Both for the fields and their operator product expansions, a well-defined limit procedure can be established. This can always be interpreted in the usual sense of multiplicative renormalization, where the renormalization factors are determined by our analysis. We also consider the limits of symmetry actions. In particular, for suitable limit states, the group of scaling transformations induces a dilation symmetry in the limit theory.
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