论文标题
Feynman使用Gröbner基地减少
Feynman integral reduction using Gröbner bases
论文作者
论文摘要
我们研究了Feynman积分将使用Gröbner基碱基降低到主体积分中，以合理的双换档代数为代数，其中逐个组合（IBP）关系形成了左侧理想。然后，可以通过计算IBP关系形成的左侧理想的gröbner基础来一劳永逸地解决将给定的积分家族降低为主积分的问题。我们在几个示例中明确证明了这一点。我们介绍了所谓的一阶正常形式IBP关系，我们通过在y modulo中减少iBP关系左侧理想的gröbner基础中的移位运算符来获得。对于更复杂的情况，如果Gröbner基础在计算上很昂贵，则我们基于函数字段的线性代数开发ANSATZ，以获得正常形式的IBP关系。
We investigate the reduction of Feynman integrals to master integrals using Gröbner bases in a rational double-shift algebra Y in which the integration-by-parts (IBP) relations form a left ideal. The problem of reducing a given family of integrals to master integrals can then be solved once and for all by computing the Gröbner basis of the left ideal formed by the IBP relations. We demonstrate this explicitly for several examples. We introduce so-called first-order normal-form IBP relations which we obtain by reducing the shift operators in Y modulo the Gröbner basis of the left ideal of IBP relations. For more complicated cases, where the Gröbner basis is computationally expensive, we develop an ansatz based on linear algebra over a function field to obtain the normal-form IBP relations.
