Copositive geometry of Feynman integrals

IF 1.4 3区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Letters in Mathematical Physics Pub Date : 2025-06-27 DOI:10.1007/s11005-025-01961-w

Bernd Sturmfels, Máté L. Telek

引用次数: 0

Abstract

Copositive matrices and copositive polynomials are objects from optimization. We connect these to the geometry of Feynman integrals in physics. The integral is guaranteed to converge if its kinematic parameters lie in the copositive cone. Pólya’s method makes this manifest. We study the copositive cone for the second Symanzik polynomial of any Feynman graph. Its algebraic boundary is described by Landau discriminants.

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费曼积分的共轭几何

共乘矩阵和共乘多项式是最优化研究的对象。我们把这些和物理学中费曼积分的几何联系起来。如果其运动参数位于复合锥内，则保证积分收敛。Pólya的方法使其变得明显。研究了任意Feynman图的第二个Symanzik多项式的共合锥。它的代数边界由朗道判别式描述。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Letters in Mathematical Physics 物理-物理：数学物理

CiteScore

2.40

自引率

8.30%

发文量

111

审稿时长

3 months

期刊介绍： The aim of Letters in Mathematical Physics is to attract the community''s attention on important and original developments in the area of mathematical physics and contemporary theoretical physics. The journal publishes letters and longer research articles, occasionally also articles containing topical reviews. We are committed to both fast publication and careful refereeing. In addition, the journal offers important contributions to modern mathematics in fields which have a potential physical application, and important developments in theoretical physics which have potential mathematical impact.