Dodgson polynomials appear in Schwinger parametric Feynman integrals and are closely related to the well known Kirchhoff (or first Symanzik) polynomial. In this article a new combinatorial interpretation and a generalisation of Dodgson polynomials are provided. This leads to two new identities that relate large sums of products of Dodgson polynomials to a much simpler expression involving powers of the Kirchhoff polynomial. These identities can be applied to the parametric integrand for quantum electrodynamics, simplifying it significantly. This is worked out here in detail on the example of superficially renormalised photon propagator Feynman graphs, but works much more generally.

中文翻译：

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道奇森多项式恒等式

Dodgson 多项式出现在 Schwinger 参数费曼积分中，并且与众所周知的 Kirchhoff（或第一个 Symanzik）多项式密切相关。在本文中，提供了一种新的组合解释和 Dodgson 多项式的推广。这导致了两个新的恒等式，它们将 Dodgson 多项式的大量乘积与涉及基尔霍夫多项式的幂的更简单的表达式相关联。这些恒等式可以应用于量子电动力学的参数被积函数，从而显着简化它。这是在表面重整化光子传播费曼图的例子中详细计算出来的，但工作得更普遍。