Feynman积分的Cohen-Macaulay性质
Cohen-Macaulay Property of Feynman Integrals
摘要：
费曼积分和GKZ $A$ -超几何系统之间的连接一直是最近的兴趣与数学技术的进步和计算工具打开新的可能性的话题，在本文中，我们继续探讨这种连接。对于每一个这样的超几何系统，都有一个相应的环面理想，我们证明了后者对于两个大的Feynman积分族具有Cohen-Macaulay性质。这意味着，例如，独立的解决方案和动力学奇点的数量是独立的时空维度和广义传播子的权力。此外，特别是，这意味着找到这些积分的级数表示的过程是完全算法的。
英文摘要：
The connection between Feynman integrals and GKZ $A$-hypergeometric systems has been a topic of recent interest with advances in mathematical techniques and computational tools opening new possibilities; in this paper we continue to explore this connection. To each such hypergeometric system there is an associated toric ideal, we prove that the latter has the Cohen-Macaulay property for two large families of Feynman integrals. This implies, for example, that both the number of independent solutions and dynamical singularities are independent of space-time dimension and generalized propagator powers. Furthermore, in particular, it means that the process of finding a series representation of these integrals is fully algorithmic.
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