几何关联的动量截断和量纲正则化
Geometrically relating momentum cut-off and dimensional regularization
摘要：
标量场理论的$β$函数描述了耦合常数对重整化质量尺度的依赖关系。这种依赖性受到正则化方案的选择的影响。本文利用标量场理论的费曼图的Hopf代数，通过规范变换，将动量截断正则化和维数正则化的$β$ -函数明确地联系起来。
英文摘要：
The $β$ function for a scalar field theory describes the dependence of the coupling constant on the renormalization mass scale. This dependence is affected by the choice of regularization scheme. I explicitly relate the $β$-functions of momentum cut-off regularization and dimensional regularization on scalar field theories by a gauge transformation using the Hopf algebras of the Feynman diagrams of the theories.
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