Equivalence of first and second order formulations of the Einstein-Hilbert theory

Abstract

We derive a general relation between the background effective actions, which directly proves that the two formulations of the Einstein-Hilbert theory with background fields are equivalent at the quantum level. This basic result has been substantiated in a general background gauge, by explicit calculations at one-loop order of the corresponding counterterm Lagrangians.

arXiv comment21 pages, 2 figures

References in corpus (23)

• Physical Aspects of the Space-Time Torsion
• On the equivalence of the Einstein-Hilbert and the Einstein-Palatini formulations of general relativity for an arbitrary connection
• Tracing the high energy theory of gravity: an introduction to Palatini inflation
• Gauge invariant renormalizability of quantum gravity
• Feynman rules and beta-function for the BF Yang-Mills Theory
• Coupling Metric-Affine Gravity to the Standard Model and Dark Matter Fermions
• Background gauge renormalization and BRST identities
• A Canonical Analysis of the Einstein-Hilbert Action in First Order Form
• Perturbative Calculations with the First Order Form of Gauge Theories
• Radiative Corrections and the Palatini Action
• The Canonical Structure of the First Order Einstein-Hilbert Action
• BRST renormalization of the first order Yang-Mill theory
• The One-Loop Divergences of the Linear Gravity with the Torsion Terms
• A correspondence between $1^{st}$ and $2^{nd}$ order formalism by a metricity constraint
• Renormalization of Hamiltonian QCD
• Quantization of Einstein-Cartan theory in the first order form
• Covariant quantization of Yang-Mills theory in the first order formalism
• Structural identities in the first order formulation of quantum gravity
• Quantum gravity in a general background gauge
• Consistency Conditions for the First-Order Formulation of Yang-Mills Theory
• Cohomology and Renormalization of BFYM Theory in three Dimensions
• First order formulation of the Yang-Mills theory in a background field
• Renormalization of the Einstein-Cartan Theory in First-Order Form

Cited by in corpus (2)

• Covariant quantization of the Einstein-Hilbert theory in first-order form
• FeynGrav 4.0