This article is an extension of the author’s second master thesis, Prinz (2017). It aims to introduce to the theory of perturbatively quantized General Relativity coupled to Spinor Electrodynamics, provide the results thereof and set the notation to serve as a starting point for further research in this direction. It includes the differential geometric and Hopf algebraic background, as well as the corresponding Lagrange density and some renormalization theory. Then, a particular problem in the renormalization of Quantum General Relativity coupled to Quantum Electrodynamics is addressed and solved by a generalization of Furry’s Theorem. Next, the restricted combinatorial Green’s functions for all two-loop propagators and all one-loop divergent subgraphs thereof are presented. Finally, relations between these one-loop restricted combinatorial Green’s functions necessary for multiplicative renormalization are discussed.

本文是作者第二篇硕士论文Prinz（2017）的扩展。它的目的是向与转子电动力学耦合的扰动量化广义相对论引入理论，提供其结果，并为该方向的进一步研究提供起点。它包括微分几何和Hopf代数背景，以及相应的Lagrange密度和一些重归一化理论。然后，通过Furry定理的推广，解决了与量子电动力学耦合的量子广义相对论的重新归一化中的一个特殊问题。接下来，给出了所有两环传播子及其所有单环发散子图的受限组合格林函数。最后，