Newtonian Potential in Quantum Regge Gravity

Abstract

We show how the Newtonian potential between two heavy masses can be computed in simplicial quantum gravity. On the lattice we compute correlations between Wilson lines associated with the heavy particles and which are closed by the lattice periodicity. We check that the continuum analog of this quantity reproduces the Newtonian potential in the weak field expansion. In the smooth anti-de Sitter-like phase, which is the only phase where a sensible lattice continuum limit can be constructed in this model, we attempt to determine the shape and mass dependence of the attractive potential close to the critical point in $G$. It is found that non-linear graviton interactions give rise to a potential which is Yukawa-like, with a mass parameter that decreases towards the critical point where the average curvature vanishes. In the vicinity of the critical point we give an estimate for the effective Newton constant.

(47 pages), CERN-TH.7314/94

References in corpus (9)

• Leading Quantum Correction to the Newtonian Potential
• Scaling Exponents in Quantum Gravity near Two Dimensions
• Ultraviolet Stable Fixed Point and Scaling Relations in 2+$\epsilon$ Dimensional Quantum Gravity
• Quantum Gravity, Dynamical Triangulation and Higer Derivative Regularization
• Invariant Correlations in Simplicial Gravity
• Simplicial Gravity Coupled to Scalar Matter
• Influence of the Measure on Simplicial Quantum Gravity in Four Dimensions
• On the absence of localized curvature in the weak-coupling phase of quantum gravity
• The radial gauge propagators in quantum gravity

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