24 research outputs found
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
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
Nonlocal Effective Field Equations for Quantum Cosmology
The possibility that the strength of gravitational interactions might slowly
increase with distance, is explored by formulating a set of effective field
equations, which incorporate the gravitational, vacuum-polarization induced,
running of Newton's constant . The resulting long distance (or large time)
behaviour depends on only one adjustable parameter , and the implications
for the Robertson-Walker universe are calculated, predicting an accelerated
power-law expansion at later times .Comment: 9 page
Gravitational Wilson Loop and Large Scale Curvature
In a quantum theory of gravity the gravitational Wilson loop, defined as a
suitable quantum average of a parallel transport operator around a large
near-planar loop, provides important information about the large-scale
curvature properties of the geometry. Here we shows that such properties can be
systematically computed in the strong coupling limit of lattice regularized
quantum gravity, by performing a local average over rotations, using an assumed
near-uniform measure in group space. We then relate the resulting quantum
averages to an expected semi-classical form valid for macroscopic observers,
which leads to an identification of the gravitational correlation length
appearing in the Wilson loop with an observed large-scale curvature. Our
results suggest that strongly coupled gravity leads to a positively curved (De
Sitter-like) quantum ground state, implying a positive effective cosmological
constant at large distances.Comment: 22 pages, 6 figure
Non-Perturbative Gravity and the Spin of the Lattice Graviton
The lattice formulation of quantum gravity provides a natural framework in
which non-perturbative properties of the ground state can be studied in detail.
In this paper we investigate how the lattice results relate to the continuum
semiclassical expansion about smooth manifolds. As an example we give an
explicit form for the lattice ground state wave functional for semiclassical
geometries. We then do a detailed comparison between the more recent
predictions from the lattice regularized theory, and results obtained in the
continuum for the non-trivial ultraviolet fixed point of quantum gravity found
using weak field and non-perturbative methods. In particular we focus on the
derivative of the beta function at the fixed point and the related universal
critical exponent for gravitation. Based on recently available lattice
and continuum results we assess the evidence for the presence of a massless
spin two particle in the continuum limit of the strongly coupled lattice
theory. Finally we compare the lattice prediction for the vacuum-polarization
induced weak scale dependence of the gravitational coupling with recent
calculations in the continuum, finding similar effects.Comment: 46 pages, one figur
Discrete approaches to quantum gravity in four dimensions
The construction of a consistent theory of quantum gravity is a problem in
theoretical physics that has so far defied all attempts at resolution. One
ansatz to try to obtain a non-trivial quantum theory proceeds via a
discretization of space-time and the Einstein action. I review here three major
areas of research: gauge-theoretic approaches, both in a path-integral and a
Hamiltonian formulation, quantum Regge calculus, and the method of dynamical
triangulations, confining attention to work that is strictly four-dimensional,
strictly discrete, and strictly quantum in nature.Comment: 33 pages, invited contribution to Living Reviews in Relativity; the
author welcomes any comments and suggestion
Discrete structures in gravity
Discrete approaches to gravity, both classical and quantum, are reviewed
briefly, with emphasis on the method using piecewise-linear spaces. Models of
3-dimensional quantum gravity involving 6j-symbols are then described, and
progress in generalising these models to four dimensions is discussed, as is
the relationship of these models in both three and four dimensions to
topological theories. Finally, the repercussions of the generalisations are
explored for the original formulation of discrete gravity using edge-length
variables.Comment: 30 pages, 4 figure
Renormalization Group Running of Newton's G: The Static Isotropic Case
Corrections are computed to the classical static isotropic solution of
general relativity, arising from non-perturbative quantum gravity effects. A
slow rise of the effective gravitational coupling with distance is shown to
involve a genuinely non-perturbative scale, closely connected with the
gravitational vacuum condensate, and thereby, it is argued, related to the
observed effective cosmological constant. Several analogies between the
proposed vacuum condensate picture of quantum gravitation, and non-perturbative
aspects of vacuum condensation in strongly coupled non-abelian gauge theories
are developed. In contrast to phenomenological approaches, the underlying
functional integral formulation of the theory severely constrains possible
scenarios for the renormalization group evolution of couplings. The expected
running of Newton's constant is compared to known vacuum polarization
induced effects in QED and QCD. The general analysis is then extended to a set
of covariant non-local effective field equations, intended to incorporate the
full scale dependence of , and examined in the case of the static isotropic
metric. The existence of vacuum solutions to the effective field equations in
general severely restricts the possible values of the scaling exponent .Comment: 61 pages, 3 figure
Quantum Gravity in Large Dimensions
Quantum gravity is investigated in the limit of a large number of space-time
dimensions, using as an ultraviolet regularization the simplicial lattice path
integral formulation. In the weak field limit the appropriate expansion
parameter is determined to be . For the case of a simplicial lattice dual
to a hypercube, the critical point is found at (with ) separating a weak coupling from a strong coupling phase, and with degenerate zero modes at . The strong coupling, large , phase is
then investigated by analyzing the general structure of the strong coupling
expansion in the large limit. Dominant contributions to the curvature
correlation functions are described by large closed random polygonal surfaces,
for which excluded volume effects can be neglected at large , and whose
geometry we argue can be approximated by unconstrained random surfaces in this
limit. In large dimensions the gravitational correlation length is then found
to behave as , implying for the universal
gravitational critical exponent the value at .Comment: 47 pages, 2 figure
Wheeler-DeWitt Equation in 2 + 1 Dimensions
The infrared structure of quantum gravity is explored by solving a lattice
version of the Wheeler-DeWitt equations. In the present paper only the case of
2+1 dimensions is considered. The nature of the wavefunction solutions is such
that a finite correlation length emerges and naturally cuts off any infrared
divergences. Properties of the lattice vacuum are consistent with the existence
of an ultraviolet fixed point in located at the origin, thus precluding the
existence of a weak coupling perturbative phase. The correlation length
exponent is determined exactly and found to be . The results obtained
so far lend support to the claim that the Lorentzian and Euclidean formulations
belong to the same field-theoretic universality class.Comment: 56 pages, 7 figures, typos fixed, references adde