4,726 research outputs found
A simple background-independent hamiltonian quantum model
We study formulation and probabilistic interpretation of a simple
general-relativistic hamiltonian quantum system. The system has no unitary
evolution in background time. The quantum theory yields transition
probabilities between measurable quantities (partial observables). These
converge to the classical predictions in the limit. Our main tool
is the kernel of the projector on the solutions of Wheeler-deWitt equation,
which we analyze in detail. It is a real quantity, which can be seen as a
propagator that propagates "forward" as well as "backward" in a local parameter
time. Individual quantum states, on the other hand, may contain only "forward
propagating" components. The analysis sheds some light on the interpretation of
background independent transition amplitudes in quantum gravity
Simplicial minisuperspace models in the presence of a massive scalar field with arbitrary scalar coupling
We extend previous simplicial minisuperspace models to account for arbitrary
scalar coupling \eta R\phi^2.Comment: 24 pages and 9 figures. Accepted for publication by Classical and
Quantum Gravit
Global phase time and path integral for the Kantowski--Sachs anisotropic univers
The action functional of the anisotropic Kantowski--Sachs cosmological model
is turned into that of an ordinary gauge system. Then a global phase time is
identified for the model by imposing canonical gauge conditions, and the
quantum transition amplitude is obtained by means of the usual path integral
procedure of Fadeev and Popov.Comment: 11 page
Creation of unstable particles and decoherence in semiclassical cosmology
We consider a simple cosmological model in order to show the importance of
unstable particle creation for the validity of the semiclassical approximation.
Using the mathematical structure of rigged Hilbert spaces we show that particle
creation is the seed of decoherence which enables the quantum to classical
transition.Comment: latex file; 18 pages. Some changes have been added. To appear in Gen.
Rel. and Gra
Spacetime states and covariant quantum theory
In it's usual presentation, classical mechanics appears to give time a very
special role. But it is well known that mechanics can be formulated so as to
treat the time variable on the same footing as the other variables in the
extended configuration space. Such covariant formulations are natural for
relativistic gravitational systems, where general covariance conflicts with the
notion of a preferred physical-time variable. The standard presentation of
quantum mechanics, in turns, gives again time a very special role, raising well
known difficulties for quantum gravity. Is there a covariant form of
(canonical) quantum mechanics? We observe that the preferred role of time in
quantum theory is the consequence of an idealization: that measurements are
instantaneous. Canonical quantum theory can be given a covariant form by
dropping this idealization. States prepared by non-instantaneous measurements
are described by "spacetime smeared states". The theory can be formulated in
terms of these states, without making any reference to a special time variable.
The quantum dynamics is expressed in terms of the propagator, an object
covariantly defined on the extended configuration space.Comment: 20 pages, no figures. Revision: minor corrections and references
adde
On the interpretation of time-reparametrization-invariant quantum mechanics
The classical and quantum dynamics of simple time-reparametrization-
invariant models containing two degrees of freedom are studied in detail.
Elimination of one ``clock'' variable through the Hamiltonian constraint leads
to a description of time evolution for the remaining variable which is
essentially equivalent to the standard quantum mechanics of an unconstrained
system. In contrast to a similar proposal of Rovelli, evolution is with respect
to the geometrical proper time, and the Heisenberg equation of motion is exact.
The possibility of a ``test clock'', which would reveal time evolution while
contributing negligibly to the Hamiltonian constraint is examined, and found to
be viable in the semiclassical limit of large quantum numbers.Comment: 13 pages, set in REVTeX. One figure available by FAX from
[email protected]
Quantum cosmology with a curvature squared action
The correct quantum description for a curvature squared term in the action
can be obtained by casting the action in the canonical form with the
introduction of a variable which is the negative of the first derivative of the
field variable appearing in the action, only after removing the total
derivative terms from the action. We present the Wheeler-DeWitt equation and
obtain the expression for the probability density and current density from the
equation of continuity. Furthermore, in the weak energy limit we obtain the
classical Einstein equation. Finally we present a solution of the wave
equation.Comment: 8 pages, revte
Spacetime Coarse Grainings in the Decoherent Histories Approach to Quantum Theory
We investigate the possibility of assigning consistent probabilities to sets
of histories characterized by whether they enter a particular subspace of the
Hilbert space of a closed system during a given time interval. In particular we
investigate the case that this subspace is a region of the configuration space.
This corresponds to a particular class of coarse grainings of spacetime
regions. We consider the arrival time problem and the problem of time in
reparametrization invariant theories as for example in canonical quantum
gravity. Decoherence conditions and probabilities for those application are
derived. The resulting decoherence condition does not depend on the explicit
form of the restricted propagator that was problematic for generalizations such
as application in quantum cosmology. Closely related is the problem of
tunnelling time as well as the quantum Zeno effect. Some interpretational
comments conclude, and we discuss the applicability of this formalism to deal
with the arrival time problem.Comment: 23 pages, Few changes and added references in v
A Closed Contour of Integration in Regge Calculus
The analytic structure of the Regge action on a cone in dimensions over a
boundary of arbitrary topology is determined in simplicial minisuperspace. The
minisuperspace is defined by the assignment of a single internal edge length to
all 1-simplices emanating from the cone vertex, and a single boundary edge
length to all 1-simplices lying on the boundary. The Regge action is analyzed
in the space of complex edge lengths, and it is shown that there are three
finite branch points in this complex plane. A closed contour of integration
encircling the branch points is shown to yield a convergent real wave function.
This closed contour can be deformed to a steepest descent contour for all sizes
of the bounding universe. In general, the contour yields an oscillating wave
function for universes of size greater than a critical value which depends on
the topology of the bounding universe. For values less than the critical value
the wave function exhibits exponential behaviour. It is shown that the critical
value is positive for spherical topology in arbitrary dimensions. In three
dimensions we compute the critical value for a boundary universe of arbitrary
genus, while in four and five dimensions we study examples of product manifolds
and connected sums.Comment: 16 pages, Latex, To appear in Gen. Rel. Gra
Effective Theories of Coupled Classical and Quantum Variables from Decoherent Histories: A New Approach to the Backreaction Problem
We use the decoherent histories approach to quantum theory to derive the form
of an effective theory describing the coupling of classical and quantum
variables. The derivation is carried out for a system consisting of a large
particle coupled to a small particle with the important additional feature that
the large particle is also coupled to a thermal environment producing the
decoherence necessary for classicality. The effective theory is obtained by
tracing out both the environment and the small particle variables. It consists
of a formula for the probabilities of a set of histories of the large particle,
and depends on the dynamics and initial quantum state of the small particle. It
has the form of an almost classical particle coupled to a stochastic variable
whose probabilities are determined by a formula very similar to that given by
quantum measurement theory for continuous measurements of the small particle's
position. The effective theory gives intuitively sensible answers when the
small particle is in a superposition of localized states.Comment: 27 pages, plain Te
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