This paper discusses the algorithmic generation of Feynman graphs for QFT models that have some form of explicit propagator mixing, including some related theoretical background. Primarily, it is shown that an ordinary Feynman graph generator — ie one that is able to deal with models without mixed propagators — can be employed to simulate the former, more general type of graph generation.

Most of the discussion occurs in the context of graph models — simplified versions of QFT models, that retain only the combinatorial features of the latter type of models. There is a single graph model, noted $\mathsf{M}(\mathcal{L})$, for each Lagrangian density $\mathcal{L}$ but, for each graph model M, there are infinitely many $\mathcal{L}$ such that $M=\mathsf{M}(\mathcal{L})$; hence, below, $\overline{\mathcal{L}}$ is not unique (that is not a critical issue, though, as $\overline{\mathcal{L}}$ is used mainly for explanatory purposes and the claims do not depend on the specific $\overline{\mathcal{L}}$ that may be chosen).

The aforementioned simulation relies on the construction of an appropriate graph model $\overline{M}$ from the original $\mathsf{M}(\mathcal{L})=M$, such that (i) there is $\overline{\mathcal{L}}$ without mixed propagators which satisfies $\overline{M}=\mathsf{M}(\overline{\mathcal{L}})$ (ie $\overline{M}$ is a type-${\text{SD}}^{\text{⁎}}$ model), (ii) the Feynman graphs for $\mathcal{L}$ can be easily obtained from those generated for $\overline{\mathcal{L}}$, and (iii) the symmetry factors computed for the graphs in $\overline{\mathcal{L}}$ need not be corrected (and, if some care is taken, the same applies to their signs).

本文讨论了具有某种形式的显式传播器混合的QFT 模型的费曼图的算法生成，包括一些相关的理论背景。首先，它表明一个普通的费曼图生成器——即能够在没有混合传播器的情况下处理模型的生成器——可以用来模拟前一种更通用的图生成类型。

大多数讨论发生在图模型的背景下——QFT 模型的简化版本，仅保留后一种模型的组合特征。有一个单一的图形模型，指出$\mathsf{米}(\mathcal{升})$, 对于每个拉格朗日密度 $\mathcal{升}$但是，对于每个图模型M，有无限多个$\mathcal{升}$ 以至于 $米=\mathsf{米}(\mathcal{升})$; 因此，下面，$\overline{\mathcal{升}}$ 不是唯一的（不过，这不是一个关键问题，因为 $\overline{\mathcal{升}}$ 主要用于说明目的，权利要求不依赖于具体的 $\overline{\mathcal{升}}$ 可以选择）。

上述模拟依赖于构建适​​当的图模型 $\overline{米}$ 从原来的 $\mathsf{米}(\mathcal{升})=米$, 使得 ( i ) 有$\overline{\mathcal{升}}$ 没有满足的混合传播者 $\overline{米}=\mathsf{米}(\overline{\mathcal{升}})$ （IE $\overline{米}$ 是一种类型-${\text{标清}}^{\text{⁎}}$模型），（ii）费曼图$\mathcal{升}$ 可以很容易地从那些为 $\overline{\mathcal{升}}$, 和 ( iii ) 为图计算的对称因子$\overline{\mathcal{升}}$ 不需要更正（并且，如果小心谨慎，这同样适用于它们的符号）。