961 research outputs found
Causal Sets: Quantum gravity from a fundamentally discrete spacetime
In order to construct a quantum theory of gravity, we may have to abandon
certain assumptions we were making. In particular, the concept of spacetime as
a continuum substratum is questioned. Causal Sets is an attempt to construct a
quantum theory of gravity starting with a fundamentally discrete spacetime. In
this contribution we review the whole approach, focusing on some recent
developments in the kinematics and dynamics of the approach.Comment: 10 pages, review of causal sets based on talk given at the 1st MCCQG
conferenc
Feynman Propagator for a Free Scalar Field on a Causal Set
The Feynman propagator for a free bosonic scalar field on the discrete
spacetime of a causal set is presented. The formalism includes scalar field
operators and a vacuum state which define a scalar quantum field theory on a
causal set. This work can be viewed as a novel regularisation of quantum field
theory based on a Lorentz invariant discretisation of spacetime.Comment: 4 pages, 2 plots. Minor updates to match published versio
A Distinguished Vacuum State for a Quantum Field in a Curved Spacetime: Formalism, Features, and Cosmology
We define a distinguished "ground state" or "vacuum" for a free scalar
quantum field in a globally hyperbolic region of an arbitrarily curved
spacetime. Our prescription is motivated by the recent construction of a
quantum field theory on a background causal set using only knowledge of the
retarded Green's function. We generalize that construction to continuum
spacetimes and find that it yields a distinguished vacuum or ground state for a
non-interacting, massive or massless scalar field. This state is defined for
all compact regions and for many noncompact ones. In a static spacetime we find
that our vacuum coincides with the usual ground state. We determine it also for
a radiation-filled, spatially homogeneous and isotropic cosmos, and show that
the super-horizon correlations are approximately the same as those of a thermal
state. Finally, we illustrate the inherent non-locality of our prescription
with the example of a spacetime which sandwiches a region with curvature
in-between flat initial and final regions
Gravity and Matter in Causal Set Theory
The goal of this paper is to propose an approach to the formulation of
dynamics for causal sets and coupled matter fields. We start from the continuum
version of the action for a Klein-Gordon field coupled to gravity, and rewrite
it first using quantities that have a direct correspondent in the case of a
causal set, namely volumes, causal relations, and timelike lengths, as
variables to describe the geometry. In this step, the local Lagrangian density
for a set of fields is recast into a quasilocal expression
that depends on pairs of causally related points and
is a function of the values of in the Alexandrov set defined by those
points, and whose limit as and approach a common point is .
We then describe how to discretize , and use it to define a
discrete action.Comment: 13 pages, no figures; In version 2, friendlier results than in
version 1 are obtained following much shorter derivation
Evidence for a continuum limit in causal set dynamics
We find evidence for a continuum limit of a particular causal set dynamics
which depends on only a single ``coupling constant'' and is easy to
simulate on a computer. The model in question is a stochastic process that can
also be interpreted as 1-dimensional directed percolation, or in terms of
random graphs.Comment: 24 pages, 19 figures, LaTeX, adjusted terminolog
Noise kernel for a quantum field in Schwarzschild spacetime under the Gaussian approximation
A method is given to compute an approximation to the noise kernel, defined as
the symmetrized connected 2-point function of the stress tensor, for the
conformally invariant scalar field in any spacetime conformal to an
ultra-static spacetime for the case in which the field is in a thermal state at
an arbitrary temperature. The most useful applications of the method are flat
space where the approximation is exact and Schwarzschild spacetime where the
approximation is better than it is in most other spacetimes. The two points are
assumed to be separated in a timelike or spacelike direction. The method
involves the use of a Gaussian approximation which is of the same type as that
used by Page to compute an approximate form of the stress tensor for this field
in Schwarzschild spacetime. All components of the noise kernel have been
computed exactly for hot flat space and one component is explicitly displayed.
Several components have also been computed for Schwarzschild spacetime and
again one component is explicitly displayed.Comment: 34 pages, no figures. Substantial revisions in Secs. I, IV, and V;
minor revisions elsewhere; new results include computation of the exact noise
kernel for hot flat space and an approximate computation of the noise kernel
for a thermal state at an arbitrary temperature in Schwarzschild spacetime
when the points are split in the time directio
Representations of Spacetime Alternatives and Their Classical Limits
Different quantum mechanical operators can correspond to the same classical
quantity. Hermitian operators differing only by operator ordering of the
canonical coordinates and momenta at one moment of time are the most familiar
example. Classical spacetime alternatives that extend over time can also be
represented by different quantum operators. For example, operators representing
a particular value of the time average of a dynamical variable can be
constructed in two ways: First, as the projection onto the value of the time
averaged Heisenberg picture operator for the dynamical variable. Second, as the
class operator defined by a sum over those histories of the dynamical variable
that have the specified time-averaged value. We show both by explicit example
and general argument that the predictions of these different representations
agree in the classical limit and that sets of histories represented by them
decohere in that limit.Comment: 11 pages, 10 figures, Revtex4, minor correction
Metric fluctuations of an evaporating black hole from back reaction of stress tensor fluctuations
This paper delineates the first steps in a systematic quantitative study of
the spacetime fluctuations induced by quantum fields in an evaporating black
hole under the stochastic gravity program. The central object of interest is
the noise kernel, which is the symmetrized two-point quantum correlation
function of the stress tensor operator. As a concrete example we apply it to
the study of the spherically-symmetric sector of metric perturbations around an
evaporating black hole background geometry. For macroscopic black holes we find
that those fluctuations grow and eventually become important when considering
sufficiently long periods of time (of the order of the evaporation time), but
well before the Planckian regime is reached. In addition, the assumption of a
simple correlation between the fluctuations of the energy flux crossing the
horizon and far from it, which was made in earlier work on
spherically-symmetric induced fluctuations, is carefully scrutinized and found
to be invalid. Our analysis suggests the existence of an infinite amplitude for
the fluctuations when trying to localize the horizon as a three-dimensional
hypersurface, as in the classical case, and, as a consequence, a more accurate
picture of the horizon as possessing a finite effective width due to quantum
fluctuations. This is supported by a systematic analysis of the noise kernel in
curved spacetime smeared with different functions under different conditions,
the details are collected in the appendices. This case study shows a pathway
for probing quantum metric fluctuations near the horizon and understanding
their physical meaning.Comment: 21 pages, REVTe
- …