Misc,
Algebraic Structures in the Coupling of Gravity to Gauge Theories
(2018)cite arxiv:1812.09919Comment: 57 pages, 259 Feynman diagrams, article; minor revisions; version to appear in Annals of Physics.
Abstract
This article is an extension of the author's second master thesis 1. 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.
Keywords: Quantum Field Theory; Quantum Gravity; Quantum General Relativity;
Quantum Electrodynamics; Perturbative Quantization; Hopf Algebraic
Renormalization
