2022/08/30 by David Prinz, Prinz, David · 1 citation
Physics and Astronomy · #81T13 #83C45 #83C47 #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories
paper · pdf · doi:10.48550/arxiv.2208.14166
openalex publication_date 2022/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider (effective) Quantum General Relativity coupled to the Standard Model and study its transversality. To this end, we provide all propagator and three-valent vertex Feynman rules. Then we examine the longitudinal, identical and transversal projection tensors for the de Donder gauge fixing and the Lorenz gauge fixing. In particular, we recall several identities from Quantum Yang--Mills theory and introduce their counterparts in (effective) Quantum General Relativity: This includes decompositions of the longitudinal projection tensors as well as expressions of the corresponding propagators in terms of their transversal structure, together with longitudinal contraction identities for all three-valent vertex Feynman rules. In addition, we introduce the notion of an optimal gauge fixing as the natural choice for a given gauge theory: In particular, we find that this is the de Donder gauge fixing in General Relativity and the Lorenz gauge fixing in Yang--Mills theory.