1,261 research outputs found
Space-time foam in 2D and the sum over topologies
It is well-known that the sum over topologies in quantum gravity is
ill-defined, due to a super-exponential growth of the number of geometries as a
function of the space-time volume, leading to a badly divergent gravitational
path integral. Not even in dimension 2, where a non-perturbative quantum
gravity theory can be constructed explicitly from a (regularized) path
integral, has this problem found a satisfactory solution. -- In the present
work, we extend a previous 2d Lorentzian path integral, regulated in terms of
Lorentzian random triangulations, to include space-times with an arbitrary
number of handles. We show that after the imposition of physically motivated
causality constraints, the combined sum over geometries and topologies is
well-defined and possesses a continuum limit which yields a concrete model of
space-time foam in two dimensions.Comment: 13 pages, 6 Postscript figures; contribution to the proceedings of
the Workshop on Random Geometry, Krakow, May 15-17, 200
Photon location in spacetime
The NewtonWigner basis of orthonormal localized states is generalized to
orthonormal and relativistic biorthonormal bases on an arbitrary hyperplane in
spacetime. This covariant formalism is applied to the measurement of photon
location using a hypothetical 3D array with pixels throughout space turned on
at a fixed time and a timelike 2D photon counting array detector with good time
resolution. A moving observer will see these detector arrays as rotated in
spacetime but the spacelike and timelike experiments remain distinct.Comment: Equations (18) to (21) and the relevant text deleted due to an error
in (20). This is no effect on the conclusions of the pape
Nonperturbative sum over topologies in 2D Lorentzian quantum gravity
The recent progress in the Causal Dynamical Triangulations (CDT) approach to
quantum gravity indicates that gravitation is nonperturbatively renormalizable.
We review some of the latest results in 1+1 and 3+1 dimensions with special
emphasis on the 1+1 model. In particular we discuss a nonperturbative
implementation of the sum over topologies in the gravitational path integral in
1+1 dimensions. The dynamics of this model shows that the presence of
infinitesimal wormholes leads to a decrease in the effective cosmological
constant. Similar ideas have been considered in the past by Coleman and others
in the formal setting of 4D Euclidean path integrals. A remarkable property of
the model is that in the continuum limit we obtain a finite space-time density
of microscopic wormholes without assuming fundamental discreteness. This shows
that one can in principle make sense out of a gravitational path integral
including a sum over topologies, provided one imposes suitable kinematical
restrictions on the state-space that preserve large scale causality.Comment: 10 pages, 4 figures. Talk given by S. Zohren at the Albert Einstein
Century International Conference (Paris, July 18-22 2005
Sum over topologies and double-scaling limit in 2D Lorentzian quantum gravity
We construct a combined non-perturbative path integral over geometries and
topologies for two-dimensional Lorentzian quantum gravity. The Lorentzian
structure is used in an essential way to exclude geometries with unacceptably
large causality violations. The remaining sum can be performed analytically and
possesses a unique and well-defined double-scaling limit, a property which has
eluded similar models of Euclidean quantum gravity in the past.Comment: 9 pages, 3 Postscript figures; added comments on strip versus bulk
partition functio
New aspects of two-dimensional quantum gravity
Causal dynamical triangulations (CDT) can be used as a regularization of
quantum gravity. In two dimensions the theory can be solved anlytically, even
before the cut-off is removed and one can study in detail how to take the
continuum limit. We show how the CDT theory is related to Euclidean 2d quantum
gravity (Liouville quantum gravity), how it can be generalized and how this
generalized CDT model has a string field theory representation as well as a
matrix model representationof a new kind, and finally how it examplifies the
possibility that time in quantum gravity might be the stochastic time related
to the branching of space into baby universes.Comment: Lectures presented at the 49th Cracow School of Theoretical Physics,
"Non-Perturbative Gravity and Quantum Chromodynamics", Zakopane May 31-June
10, 2009. To appear in Acta Physica Polonica B 40 (2009) 1001-103
Proper time is stochastic time in 2d quantum gravity
We show that proper time, when defined in the quantum theory of 2d gravity,
becomes identical to the stochastic time associated with the stochastic
quantization of space. This observation was first made by Kawai and
collaborators in the context of 2d Euclidean quantum gravity, but the relation
is even simpler and more transparent in he context of 2d gravity formulated in
the framework of CDT (causal dynamical triangulations).Comment: 30 pages, Talk presented at the meeting "Foundations of Space and
Time", Cape Town, 10-14 August 2009. To appear in the proceedings, CU
Topology change in causal quantum gravity
The role of topology change in a fundamental theory of quantum gravity is
still a matter of debate. However, when regarding string theory as
two-dimensional quantum gravity, topological fluctuations are essential. Here
we present a third quantization of two-dimensional surfaces based on the method
of causal dynamical triangulation (CDT). Formally, our construction is similar
to the c = 0 non-critical string field theory developed by Ishibashi, Kawai and
others, but physically it is quite distinct. Unlike in non-critical string
theory the topology change of spatial slices is well controlled and regulated
by Newton's constant.Comment: 4 pages, proceedings of the workshop JGRG 17 (Nagoya, Japan, December
2007
A Causal Alternative for c=0 Strings
We review a recently discovered continuum limit for the one-matrix model
which describes "causal" two-dimensional quantum gravity. The behaviour of the
quantum geometry in this limit is different from the quantum geometry of
Euclidean two-dimensional quantum gravity defined by taking the "standard"
continuum limit of the one-matrix model. Geodesic distance and time scale with
canonical dimensions in this new limit, contrary to the situation in Euclidean
two-dimensional quantum gravity. Remarkably, whenever we compare, the known
results of (generalized) causal dynamical triangulations are reproduced exactly
by the one-matrix model. We complement previous results by giving a geometrical
interpretation of the new model in terms of a generalization of the loop
equation of Euclidean dynamical triangulations. In addition, we discuss the
time evolution of the quantum geometry.Comment: 10 pages, 4 figures, Presented at "The 48th Cracow School of
Theoretical Physics: Aspects of Duality", June 13-22, 2008, Zakopane, Polan
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