143 research outputs found
Gravitational Wilson Loop in Discrete Quantum Gravity
Results for the gravitational Wilson loop, in particular the area law for
large loops in the strong coupling region, and the argument for an effective
positive cosmological constant discussed in a previous paper, are extended to
other proposed theories of discrete quantum gravity in the strong coupling
limit. We argue that the area law is a generic feature of almost all
non-perturbative lattice formulations, for sufficiently strong gravitational
coupling. The effects on gravitational Wilson loops of the inclusion of various
types of light matter coupled to lattice quantum gravity are discussed as well.
One finds that significant modifications to the area law can only arise from
extremely light matter particles. The paper ends with some general comments on
possible physically observable consequences.Comment: 39 pages, 10 figure
Role of a "Local" Cosmological Constant in Euclidean Quantum Gravity
In 4D non-perturbative Regge calculus a positive value of the effective
cosmological constant characterizes the collapsed phase of the system. If a
local term of the form is
added to the gravitational action, where is a subset of the
hinges and are positive constants, one expects that the volumes
, , ... tend to collapse and that the excitations of the
lattice propagating through the hinges are damped. We study
the continuum analogue of this effect. The additional term may represent
the coupling of the gravitational field to an external Bose condensate.Comment: LaTex, 18 page
On the Measure in Simplicial Gravity
Functional measures for lattice quantum gravity should agree with their
continuum counterparts in the weak field, low momentum limit. After showing
that the standard simplicial measure satisfies the above requirement, we prove
that a class of recently proposed non-local measures for lattice gravity do not
satisfy such a criterion, already to lowest order in the weak field expansion.
We argue therefore that the latter cannot represent acceptable discrete
functional measures for simplicial geometries.Comment: LaTeX, 15 pages, 2 figure
Invariant Correlations in Simplicial Gravity
Some first results are presented regarding the behavior of invariant
correlations in simplicial gravity, with an action containing both a bare
cosmological term and a lattice higher derivative term. The determination of
invariant correlations as a function of geodesic distance by numerical methods
is a difficult task, since the geodesic distance between any two points is a
function of the fluctuating background geometry, and correlation effects become
rather small for large distances. Still, a strikingly different behavior is
found for the volume and curvature correlation functions. While the first one
is found to be negative definite at large geodesic distances, the second one is
always positive for large distances. For both correlations the results are
consistent in the smooth phase with an exponential decay, turning into a power
law close to the critical point at . Such a behavior is not completely
unexpected, if the model is to reproduce the classical Einstein theory at
distances much larger than the ultraviolet cutoff scale.Comment: 27 pages, conforms to published versio
Scaling Dimensions of Lattice Quantized Gravity
I discuss a model for quantized gravitation based on the simplicial lattice
discretization. It has been studied in some detail using a comprehensive finite
size scaling analysis combined with renormalization group methods. The results
are consistent with a value for the universal critical exponent for gravitation
, and suggest a simple relationship between Newton's constant, the
gravitational correlation length and the observable average space-time
curvature. Some perhaps testable phenomenological implications are discussed,
such as the scale dependence of Newton's constant and properties of quantum
curvature fluctuations.Comment: Talk presented at the 9-th Marcel Grossman Meeting (LaTeX, 10 pages
Cosmological Density Perturbations with a Scale-Dependent Newton's G
We explore possible cosmological consequences of a running Newton's constant
, as suggested by the non-trivial ultraviolet fixed point
scenario in the quantum field-theoretic treatment of Einstein gravity with a
cosmological constant term. In particular we focus here on what possible
effects the scale-dependent coupling might have on large scale cosmological
density perturbations. Starting from a set of manifestly covariant effective
field equations derived earlier, we systematically develop the linear theory of
density perturbations for a non-relativistic, pressure-less fluid. The result
is a modified equation for the matter density contrast, which can be solved and
thus provides an estimate for the growth index parameter in the
presence of a running . We complete our analysis by comparing the fully
relativistic treatment with the corresponding results for the non-relativistic
(Newtonian) case, the latter also with a weakly scale dependent .Comment: 54 pages, 4 figure
The Well-Defined Phase of Simplicial Quantum Gravity in Four Dimensions
We analyze simplicial quantum gravity in four dimensions using the Regge
approach. The existence of an entropy dominated phase with small negative
curvature is investigated in detail. It turns out that observables of the
system possess finite expectation values although the Einstein-Hilbert action
is unbounded. This well-defined phase is found to be stable for a one-parameter
family of measures. A preliminary study indicates that the influence of the
lattice size on the average curvature is small. We compare our results with
those obtained by dynamical triangulation and find qualitative correspondence.Comment: 29 pages, uuencoded postscript file; to appear in Phys. Rev.
SU(2) potentials in quantum gravity
We present investigations of the potential between static charges from a
simulation of quantum gravity coupled to an SU(2) gauge field on and simplicial lattices. In the well-defined phase of the
gravity sector where geometrical expectation values are stable, we study the
correlations of Polyakov loops and extract the corresponding potentials between
a source and sink separated by a distance . In the confined phase, the
potential has a linear form while in the deconfined phase, a screened Coulombic
behavior is found. Our results indicate that quantum gravitational effects do
not destroy confinement due to non-abelian gauge fields.Comment: 3 pages, contribution to Lattice 94 conference, uuencoded compressed
postscript fil
Two-Point Functions of Four-Dimensional Simplicial Quantum Gravity
We investigate the interaction mechanism of pure quantum gravity in Regge
discretization. We compute volume-volume and link-link correlation functions.
In a preliminary analysis the forces turn out to be of Yukawa type, at least on
our finite lattice being away from the continuum limit.Comment: 3 pages, uuencoded postscript file; Proceedings of the XI
International Symposion on Lattice Field Theory, Dallas, Oct. 199
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