60 research outputs found
The trace left by signature-change-induced compactification
Recently, it has been shown that an infinite succession of classical
signature changes (''signature oscillations'') can compactify and stabilize
internal dimensions, and simultaneously leads, after a coarse graining type of
average procedure, to an effective (''physical'') space-time geometry
displaying the usual Lorentzian metric signature. Here, we consider a minimally
coupled scalar field on such an oscillating background and study its effective
dynamics. It turns out that the resulting field equation in four dimensions
contains a coupling to some non-metric structure, the imprint of the
''microscopic'' signature oscillations on the effective properties of matter.
In a multidimensional FRW model, this structure is identical to a massive
scalar field evolving in its homogeneous mode.Comment: 15 pages, LaTeX, no figure
Gravity and Signature Change
The use of proper ``time'' to describe classical ``spacetimes'' which contain
both Euclidean and Lorentzian regions permits the introduction of smooth
(generalized) orthonormal frames. This remarkable fact permits one to describe
both a variational treatment of Einstein's equations and distribution theory
using straightforward generalizations of the standard treatments for constant
signature.Comment: Plain TeX, 6 pages; to appear in GR
Closed Strings with Low Harmonics and Kinks
Low-harmonic formulas for closed relativistic strings are given. General
parametrizations are presented for the addition of second- and third-harmonic
waves to the fundamental wave. The method of determination of the
parametrizations is based upon a product representation found for the finite
Fourier series of string motion in which the constraints are automatically
satisfied. The construction of strings with kinks is discussed, including
examples. A procedure is laid out for the representation of kinks that arise
from self-intersection, and subsequent intercommutation, for harmonically
parametrized cosmic strings.Comment: 39, CWRUTH-93-
On metric-connection compatibility and the signature change of space-time
We discuss and investigate the problem of existence of metric-compatible
linear connections for a given space-time metric which is, generally, assumed
to be semi-pseudo-Riemannian. We prove that under sufficiently general
conditions such connections exist iff the rank and signature of the metric are
constant. On this base we analyze possible changes of the space-time signature.Comment: 18 standard LaTeX 2e pages. The packages AMS-LaTeX and amsfonts are
require
Dimensionality, topology, energy, the cosmological constant, and signature change
Using the concept of real tunneling configurations (classical signature
change) and nucleation energy, we explore the consequences of an alternative
minimization procedure for the Euclidean action in multiple-dimensional quantum
cosmology. In both standard Hartle-Hawking type as well as Coleman type
wormhole-based approaches, it is suggested that the action should be minimized
among configurations of equal energy. In a simplified model, allowing for
arbitrary products of spheres as Euclidean solutions, the favoured space-time
dimension is 4, the global topology of spacelike slices being (hence predicting a universe of Kantowski-Sachs type). There is,
however, some freedom for a Kaluza-Klein scenario, in which case the observed
spacelike slices are . In this case, the internal space is a product
of two-spheres, and the total space-time dimension is 6, 8, 10 or 12.Comment: 34 pages, LaTeX, no figure
Cosmological perturbations and classical change of signature
Cosmological perturbations on a manifold admitting signature change are
studied. The background solution consists in a Friedmann-Lemaitre-Robertson-
Walker (FLRW) Universe filled by a constant scalar field playing the role of a
cosmological constant. It is shown that no regular solution exist satisfying
the junction conditions at the surface of change. The comparison with similar
studies in quantum cosmology is made.Comment: 35 pages, latex, 2 figures available at [email protected], to
appear in Physical Review
Probabilities in Quantum Cosmological Models: A Decoherent Histories Analysis Using a Complex Potential
In the quantization of simple cosmological models (minisuperspace models)
described by the Wheeler-DeWitt equation, an important step is the
construction, from the wave function, of a probability distribution answering
various questions of physical interest, such as the probability of the system
entering a given region of configuration space at any stage in its entire
history. A standard but heuristic procedure is to use the flux of (components
of) the wave function in a WKB approximation. This gives sensible semiclassical
results but lacks an underlying operator formalism. In this paper, we address
the issue of constructing probability distributions linked to the
Wheeler-DeWitt equation using the decoherent histories approach to quantum
theory. We show that the appropriate class operators (the generalization of
strings of projectors) in quantum cosmology are readily constructed using a
complex potential. We derive the class operator for entering or not entering
one or more regions in configuration space. They commute with the Hamiltonian,
have a sensible classical limit and are closely related to intersection number
operators. We show that oscillatory WKB solutions to the Wheeler-DeWitt
equation give approximate decoherence of histories, as do superpositions of WKB
solutions, as long as the regions of configuration space are sufficiently
large. The corresponding probabilities coincide, in a semiclassical
approximation, with standard heuristic procedures. In brief, we exhibit the
well-defined operator formalism underlying the usual heuristic interpretational
methods in quantum cosmology.Comment: 49 pages, Latex, 8 figure
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
Quantum creation and inflationary universes: a critical appraisal
We contrast the possibility of inflation starting a) from the universe's
inception or b) from an earlier non-inflationary state. Neither case is ideal
since a) assumes quantum mechanical reasoning is straightforwardly applicable
to the early universe; while case b) requires that a singularity still be
present. Further, in agreement with Vachaspati and Trodden [1] case b) can only
solve the horizon problem if the non-inflationary phase has equation of state
.Comment: 21 pages Late
Invariant class operators in the decoherent histories analysis of timeless quantum theories
The decoherent histories approach to quantum theory is applied to a class of reparametrization invariant models, which includes systems described by the Klein-Gordon equation, and by a minisuperspace Wheeler-DeWitt equation. A key step in this approach is the construction of class operators characterizing the questions of physical interest, such as the probability of the system entering a given region of configuration space without regard to time. In non-relativistic quantum mechanics these class operators are given by time-ordered products of projection operators. But in reparametrization invariant models, where there is no time, the construction of the class operators is more complicated, the main difficulty being to find operators which commute with the Hamiltonian constraint (and so respect the invariance of the theory). Here, inspired by classical considerations, we put forward a proposal for the construction of such class operators for a class of reparametrization-invariant systems. They consist of continuous infinite temporal products of Heisenberg picture projection operators. We investigate the consequences of this proposal in a number of simple models and also compare with the evolving constants method
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