Solving the Effective Field Equations for the Newtonian Potential

R. P. Woodard (University of Florida); SoHyun Park

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Solving the Effective Field Equations for the Newtonian Potential

Sohyun Park, R. P. Woodard (University of Florida)

General Relativity and Quantum Cosmology · Submitted 15 Jul 2010

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The authors' main claim In this study we show how the Schwinger-Keldysh effective field equations can be used to compute loop corrections to the potential in a way which parallels the classical treatment.

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arXiv ID1007.2662 (version 1)

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CitationR. P. Woodard (University of Florida), SoHyun Park. "Solving the Effective Field Equations for the Newtonian Potential." arXiv:1007.2662 (2010). https://pith.science/paper/PN5SR3JF

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Loop corrections to the gravitational potential are usually inferred from scattering amplitudes, which seems quite different from how the linearized Einstein equations are solved with a static, point mass to give the classical potential. In this study we show how the Schwinger-Keldysh effective field equations can be used to compute loop corrections to the potential in a way which parallels the classical treatment. We derive explicit results for the one loop correction from the graviton self-energy induced by a massless, minimally coupled scalar.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Loop corrections to the gravitational potential are usually inferred from scattering amplitudes, which seems quite different from how the linearized Einstein equations are solved with a static, point mass to give the classical potential.	background 0.99	0.05	0.04	asserted 0.82
s1	In this study we show how the Schwinger-Keldysh effective field equations can be used to compute loop corrections to the potential in a way which parallels the classical treatment.	contribution 0.93	0.93	0.77	asserted 1.00
s2	We derive explicit results for the one loop correction from the graviton self-energy induced by a massless, minimally coupled scalar.	result 0.80	0.96	0.19	asserted 1.00

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Original abstract

Loop corrections to the gravitational potential are usually inferred from scattering amplitudes, which seems quite different from how the linearized Einstein equations are solved with a static, point mass to give the classical potential. In this study we show how the Schwinger-Keldysh effective field equations can be used to compute loop corrections to the potential in a way which parallels the classical treatment. We derive explicit results for the one loop correction from the graviton self-energy induced by a massless, minimally coupled scalar.

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19 arXiv papers cite this in 47 sentences

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Papers citing it · 27 sentences without a confident label

Builds on it 1 paper

This is the generalization of the graviton vacuum polarization induced by a minimally coupled scalar ($ξ=0$) calculated by Park and Woodard in [ref] to the case of a massless, nonminimally coupled, scalar ($ξ≠0$), and it is one of the main results of this work.

Time transients in the quantum corrected Newtonian potential induced by a massless nonminimally coupled scalar field · Non-local contributions · 1.00

Uses its method or tool 1 paper

The procedure in this case is to compute first the graviton self-energy up to one-loop order in the given field, which is needed for the effective field equations, and then compute the gravitational response to a massive point source [ref] .

Quantum corrections to the gravitational potentials of a point source due to conformal fields in de Sitter · Introduction · 0.80

Compares with it 6 papers

Comparing, however, with Park and Woodard [ref] , which calculate the effect of a minimally coupled scalar only, our results agree perfectly.

Time transients in the quantum corrected Newtonian potential induced by a massless nonminimally coupled scalar field · The Quantum Corrected Newtonian potential · 1.00
The first terms in Eqs. ([ref]–[ref]) represent the one-loop contributions from a conformal scalar field, and in the limit when $H→0, a→1$ they reduce to the Minkowski space results of Refs. [ref] , representing a nontrivial check of our principal results ([ref]–[ref]).

Quantum Scalar Corrections to the Gravitational Potentials on de Sitter Background · Computing the one-loop source integrals · 0.88
Substituting also $κ^2 = 16 πG_N$, we get [equation] which is exactly the value computed in flat space by reconstructing the potential from scattering data and effective field equations [ref] .

Quantum corrections to the gravitational potentials of a point source due to conformal fields in de Sitter · The flat-space limit · 0.91

Cites it as support 1 paper

In other words, the in-out effective action does not generate the correct quantum corrected equations of motion for the real scalar field [ref] .

A Causal Alternative to Feynman's Propagator · Introduction · 0.97

Cites it as background 6 papers

Integrals over the initial value surface are ubiquitous in computations using the Schwinger-Keldysh formalism [ref] , and much has been learned from all this experience.

Covariant Vacuum Polarizations on de Sitter Background · A Paradox from the Effective Field Equations · 0.85
One important prediction that can be made in this way are quantum corrections to the Newtonian gravitational potential, which have been studied by many authors [ref] .

Graviton corrections to the Newtonian potential using invariant observables · Introduction · 0.95
The quantum-corrected Newtonian potential including loops of different fields is by now known for free scalar, spinor and vector fields [ref] , and for the more complicated case of graviton fields [ref] .

Quantum corrections to the gravitational potentials of a point source due to conformal fields in de Sitter · Introduction · 0.88

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