重正化：一个数论模型
Renormalization : A number theoretical model
摘要：
分析了算术数论函数的Dirichlet卷积环.由于乘积和余积不具有完全乘法性，所以它在对角线上不是一个Hopf代数。可以建立一个相关的Hopf代数，但是它超过了对角线。我们认为，在量子场论重整化机制是仿照相同的原则。因此，奇异性作为对角线上的（现在连续索引的）过度计数而出现。重整化由从辅助Hopf代数到较弱乘法结构的映射给出，称为Hopf代数，重新标度对角线。
英文摘要：
We analyse the Dirichlet convolution ring of arithmetic number theoretic functions. It turns out to fail to be a Hopf algebra on the diagonal, due to the lack of complete multiplicativity of the product and coproduct. A related Hopf algebra can be established, which however overcounts the diagonal. We argue that the mechanism of renormalization in quantum field theory is modelled after the same principle. Singularities hence arise as a (now continuously indexed) overcounting on the diagonals. Renormalization is given by the map from the auxiliary Hopf algebra to the weaker multiplicative structure, called Hopf gebra, rescaling the diagonals.
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