论文标题
平方根的合理性
Rationalizability of square roots
论文作者
论文摘要
理论高能物理学中的Feynman积分计算经常涉及运动变量中的平方根。物理学家通常想根据多个多聚阶层来解决Feynman积分。从这些功能方面获得解决方案的一种方法是通过合适的变量更改合理化所有发生的正方形根。在本文中，我们对多项式比率平方根的合理性给出了严格的定义。我们表明，决定是否可以从几何学术语重新重新制定一个平方根的问题。使用这种方法，我们提供了简单的标准，可以在一个和两个变量的大多数方形根部中确定合理性。我们还提供了部分结果和策略，以证明或反驳一组方形的合理性。我们将结果应用于高能粒子物理中实际计算的许多示例。
Feynman integral computations in theoretical high energy particle physics frequently involve square roots in the kinematic variables. Physicists often want to solve Feynman integrals in terms of multiple polylogarithms. One way to obtain a solution in terms of these functions is to rationalize all occurring square roots by a suitable variable change. In this paper, we give a rigorous definition of rationalizability for square roots of ratios of polynomials. We show that the problem of deciding whether a single square root is rationalizable can be reformulated in geometrical terms. Using this approach, we give easy criteria to decide rationalizability in most cases of square roots in one and two variables. We also give partial results and strategies to prove or disprove rationalizability of sets of square roots. We apply the results to many examples from actual computations in high energy particle physics.
