1,910 research outputs found
Newtonian Potential in Quantum Regge Gravity
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 . 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.Comment: (47 pages), CERN-TH.7314/9
The asymptotics of an amplitude for the 4-simplex
An expression for the oscillatory part of an asymptotic formula for the
relativistic spin network amplitude for a 4-simplex is given. The amplitude
depends on specified areas for each two-dimensional face in the 4-simplex. The
asymptotic formula has a contribution from each flat Euclidean metric on the
4-simplex which agrees with the given areas. The oscillatory part of each
contribution is determined by the Regge calculus Einstein action for that
geometry.Comment: 5 pages amstex, typos correcte
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