Gravity-Matter Feynman Rules for any Valence

Abstract

This article derives and presents the Feynman rules for (effective) Quantum General Relativity coupled to the Standard Model for any vertex valence and with general gauge parameter $\zeta$. The results are worked out for the metric decomposition $g_{\mu \nu }={\eta }_{\mu \nu }+\varkappa h_{\mu \nu }$, a linearized de Donder gauge fixing and four dimensions of spacetime. To this end, we calculate the Feynman rules for gravitons, graviton-ghosts and for the couplings of gravitons to scalars, spinors, gauge bosons and gauge ghosts.

arXiv comment41 pages, article; minor revisions and added material; version to appear in Classical and Quantum Gravity

References in corpus (29)

• General relativity as an effective field theory: The leading quantum corrections
• New Relations for Gauge-Theory Amplitudes
• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy
• Renormalization of gauge fields: A Hopf algebra approach
• Factorization and polarization in linearized gravity
• Notes for a brief history of quantum gravity
• A resource for signs and Feynman diagrams of the Standard Model
• Anatomy of a gauge theory
• Recursive relations in the core Hopf algebra
• Gravitational Corrections to Yukawa and Phi^4 Interactions
• The 6th Post-Newtonian Potential Terms at $O(G_N^4)$
• Hidden Simplicity of the Gravity Action
• The Hopf algebra of Feynman graphs in QED
• The Two-Loop Four-Graviton Scattering Amplitudes
• Renormalization in quantum field theory and the Riemann-Hilbert problem
• Quantization of gauge fields, graph polynomials and graph cohomology
• The structure of renormalization Hopf algebras for gauge theories I: Representing Feynman graphs on BV-algebras
• Cutkosky Rules and Outer Space
• A remark on quantum gravity
• The diffeomorphism group of a non-compact orbifold
• No Lee-Wick Fields out of Gravity
• On the `simple' form of the gravitational action and the self-interacting graviton
• The Corolla Polynomial for spontaneously broken Gauge Theories
• Gauge Symmetries and Renormalization
• Complexes of marked graphs in gauge theory
• Algebraic Structures in the Coupling of Gravity to Gauge Theories
• Off-shell Diagrammatics for Quantum Gravity
• $\mathcal{N}=1$ super Feynman rules for any superspin: Noncanonical SUSY

Cited by in corpus (7)

• The Schwarzschild-Tangherlini metric from scattering amplitudes in various dimensions
• FeynGrav : FeynCalc extension for gravity amplitudes
• Lie Theory for Asymptotic Symmetries in General Relativity: The BMS Group
• Gauge Symmetries and Renormalization
• FeynMG: a FeynRules extension for scalar-tensor theories of gravity
• Lie Theory for Asymptotic Symmetries in General Relativity: The NU Group
• Scalaron Decay in Perturbative Quantum Gravity