Effective Field Theory of Gravity: Leading Quantum Gravitational Corrections to Newtons and Coulombs Law

Abstract

In this paper we consider general relativity and its combination with scalar quantum electrodynamics (QED) as an effective quantum field theory at energies well below the Planck scale. This enables us to compute the one-loop quantum corrections to the Newton and Coulomb potential induced by the combination of graviton and photon fluctuations. We derive the relevant Feynman rules and compute the nonanalytical contributions to the one-loop scattering matrix for charged scalars in the nonrelativistic limit. In particular, we derive the post-Newtonian corrections of order $Gm/{\text{c}}^{2}r$ from general relativity and the genuine quantum corrections of order $G\hslash /{\text{c}}^3{r}^2$.

14 pages, 12 figures

References in corpus (11)

• General relativity as an effective field theory: The leading quantum corrections
• Leading Quantum Correction to the Newtonian Potential
• Quantum Gravitational Corrections to the Nonrelativistic Scattering Potential of Two Masses
• Quantum Corrections to the Schwarzschild and Kerr Metrics
• On the Quantum Corrections to the Newtonian Potential
• Long Range Forces in Quantum Gravity
• Gravitational interaction to one loop in effective quantum gravity
• Leading quantum gravitational corrections to scalar QED
• Running Coupling Constants, Newtonian Potential and non localities in the Effective Action
• Leading quantum gravitational corrections to QED
• On the notion of potential in quantum gravity

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