论文标题
通过同位素技术的动量太空方程
Momentum Space Landau Equations Via Isotopy Techniques
论文作者
论文摘要
我们研究了由Quadrics有限结合的积分定义的函数的分析结构。主要动机来自属于此类的Feynman积分。使用同位素技术，我们从Feynman积分理论中得出动量空间中的Landau方程，并将这些方程式推广到自然包含第二种类型的奇点。为此，我们介绍了二次形式的分析家族的正规化，渲染适用的同位素技术。在Feynman积分的情况下，我们对主要分支的行为的了解，其中只有Landau方程的特定解决方案有助于非分析点。最后，我们讨论与重新归一化的兼容性。
We investigate the analytic structure of functions defined by integrals with integrands singular on a finite union of quadrics. The main motivation comes from Feynman integrals which belong to this class. Using isotopy techniques we derive the Landau equations in momentum space from the theory of Feynman integrals and generalize these equations to naturally include singularities of the second type. For this purpose we introduce a regularization of analytic families of quadratic forms rendering the isotopy techniques applicable. In the case of Feynman integrals we comment on what is known about the behavior on the principal branch where only specific solutions of the Landau equations contribute to non-analytic points. Finally we discuss compatibility with renormalization.
