52 research outputs found
The radial gauge propagators in quantum gravity
We give a general procedure for extracting the propagators in gauge theories
in presence of a sharp gauge fixing and we apply it to derive the propagators
in quantum gravity in the radial gauge, both in the first and in the second
order formalism in any space-time dimension. In the three dimensional case such
propagators vanish except for singular collinear contributions, in agreement
with the absence of propagating gravitons.Comment: 38 pages, 1 fig. not available, LATEX, IFUP-TH-30/9
Wilson loops in four-dimensional quantum gravity
A Wilson loop is defined, in 4-D pure Einstein gravity, as the trace of the
holonomy of the Christoffel connection or of the spin connection, and its
invariance under the symmetry transformations of the action is showed
(diffeomorphisms and local Lorentz transformations). We then compute the loop
perturbatively, both on a flat background and in the presence of an external
source; we also allow some modifications in the form of the action, and test
the action of ``stabilized'' gravity. A geometrical analysis of the results in
terms of the gauge group of the euclidean theory, , leads us to the
conclusion that the correspondent statistical system does not develope any
configuration with localized curvature at low temperature. This ``non-local''
behavior of the quantized gravitational field strongly contrasts with that of
usual gauge fields. Our results also provide an explanation for the absence of
any invariant correlation of the curvature in the same approximation.Comment: 19 pages, LaTex, report CTP #2225, June 199
Closed time like curve and the energy condition in 2+1 dimensional gravity
We consider gravity in 2+1 dimensions in presence of extended stationary
sources with rotational symmetry. We prove by direct use of Einstein's
equations that if i) the energy momentum tensor satisfies the weak energy
condition, ii) the universe is open (conical at space infinity), iii) there are
no CTC at space infinity, then there are no CTC at all.Comment: 10 pages (REVTEX 3.0), IFUP-60/9
Vacuum correlations at geodesic distance in quantum gravity
The vacuum correlations of the gravitational field are highly non-trivial to
be defined and computed, as soon as their arguments and indices do not belong
to a background but become dynamical quantities. Their knowledge is essential
however in order to understand some physical properties of quantum gravity,
like virtual excitations and the possibility of a continuum limit for lattice
theory. In this review the most recent perturbative and non-perturbative
advances in this field are presented. (To appear on Riv. Nuovo Cim.)Comment: report U.T.F. 332, July 94. Plain TeX, 67 pp. (+ 1 table and 7
figures, available from the author
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
Nonperturbative Evolution Equation for Quantum Gravity
A scale--dependent effective action for gravity is introduced and an exact
nonperturbative evolution equation is derived which governs its renormalization
group flow. It is invariant under general coordinate transformations and
satisfies modified BRS Ward--Identities. The evolution equation is solved for a
simple truncation of the space of actions. In 2+epsilon dimensions,
nonperturbative corrections to the beta--function of Newton's constant are
derived and its dependence on the cosmological constant is investigated. In 4
dimensions, Einstein gravity is found to be ``antiscreening'', i.e., Newton's
constant increases at large distances.Comment: 35 pages, late
- …