NDIM中的无质量双环“主”和三环两点函数
Massless two-loop "master" and three-loop two point function in NDIM
摘要：
NDIM（Negative Dimensional Integration Method）是一种基于解析延拓概念的计算费曼积分的方法。该方法已成功地应用于协变和非协变规范场相互作用中的许多图形，并已显示出其作为处理量子场论中费曼环积分的一种强有力的技术的实用性。原则上NDIM可以处理任何循环计算;然而，在实践中，产生的多个变量的多序列一般不能方便地总结，其分析性质通常是未知的。另一种方法是使用逐阶（循环）积分，其中第一个积分是三角图类型。然而，这种幼稚的动量积分会导致错误的结果。在这里，我们使用NDIM中的三角形的缩短版本，它适合于一个循环的循环计算，并表明它导致（经过适当的解析延拓到正维）与已知的结果一致的双循环主图。从它，一个三回路，然后计算和再次显示其与已经公布的结果，这样的图的一致性。
英文摘要：
NDIM (Negative Dimensional Integration Method) is a technique for evaluating Feynman integrals based on the concept of analytic continuation. The method has been successfully applied to many diagrams in covariant and noncovariant gauge field interactions and has shown its utility as a powerful technique to handle Feynman loop integrations in quantum field theories. In principle NDIM can handle any loop calculation; however, in practical terms, the resulting multiseries with several variables in general cannot be summed up conveniently and its analytic properties are generally unknown. The alternative then is to use order by order (loop by loop) integration in which the first integral is of the triangle diagram type. However, the naïve momentum integration of this leads to wrong results. Here we use the shortened version for the triangle in NDIM that is suitable for a loop by loop calculation and show that it leads (after appropriate analytic continuation to positive dimension) to agreement with the known result for the two-loop master diagram. From it, a three-loop is then calculated and shown again its consistency with the already published result for such a diagram.
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