Algebraic structures in the coupling of gravity to gauge theories. (English) Zbl 1457.83017
Summary: This article is an extension of the author’s second master thesis, [Algebraic structures in the coupling of gravity to gauge theories. Berlin: Humboldt-Universität (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.
MSC:
| 83C45 | Quantization of the gravitational field |
| 81V10 | Electromagnetic interaction; quantum electrodynamics |
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 81R25 | Spinor and twistor methods applied to problems in quantum theory |
| 83C60 | Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism |
Keywords:
quantum field theory; quantum gravity; quantum general relativity; quantum electrodynamics; perturbative quantization; Hopf algebraic renormalizationReferences:
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