对于费曼积分的关键点和 syzygies
1Department of Physics and Astronomy, Ghent University, Proeftuinstraat 86, Ghent, Belgium.
概括
我们在费曼积分中介绍了用于计算整合-按-部分关系的关键syzygies. 这些关键的syzygies简化了积分缩小,在量子场论计算中提供了一个新的几何视角.
科学领域:
- 理论物理 理论物理
- 高能物理 高能物理
- 数学物理 数学物理
背景情况:
- 整合按部分 (IBP) 关系对于简化量子场论中的费曼积分至关重要.
- 计算IBP关系的现有方法可能是计算密集的.
- 了解底层的理论结构是开发更有效方法的关键.
研究的目的:
- 为了研究一个新的理论结构计算整合-by-parts关系.
- 介绍和分析的概念的概念.
主要方法:
- 基于Syzygy的方法是可以使用的.
- 交点理论的交点理论.
- 对尺寸规范化的大ε极限进行分析.
- 确定贝科夫多项式对数的临界位置.
主要成果:
- 总衍生品在大ε极限的临界位置上消失.
- "关键性阴病"被确定为阴病的一个关键子集.
- 当关键位置被隔离时,关键的syzygies产生了足够的总导数来实现整体减小.
- 一个循环的分析研究和两个循环的数值构造.
结论:
- 关键的syzygies提供了一个强大的工具,以实现整体的减少.
- 这项研究为整合各部分关系提供了一个新的几何视角.
- 这种方法适用于复杂的,尖端的双循环计算.
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