157 research outputs found
The interpretation of the solutions of the Wheeler De Witt equation
We extract transition amplitudes among matter constituents of the universe
from the solutions of the Wheeler De Witt equation. The physical interpretation
of these solutions is then reached by an analysis of the properties of the
transition amplitudes. The interpretation so obtained is based on the current
carried by these solutions and confirms ideas put forward by Vilenkin.Comment: 11 pages, latex, no figure
Hawking radiation in dispersive theories, the two regimes
We compute the black hole radiation spectrum in the presence of
high-frequency dispersion in a large set of situations. In all cases, the
spectrum diverges like the inverse of the Killing frequency. When studying the
low-frequency spectrum, we find only two regimes: an adiabatic one where the
corrections with respect to the standard temperature are small, and an abrupt
one regulated by dispersion, in which the near-horizon metric can be replaced
by step functions. The transition from one regime to the other is governed by a
single parameter which also governs the net redshift undergone by dispersive
modes. These results can be used to characterize the quasiparticles spectrum of
recent and future experiments aiming to detect the analogue Hawking radiation.
They also apply to theories of quantum gravity which violate Lorentz
invariance.Comment: 11 pages, 9 figure
Particle creation and non-adiabatic transitions in quantum cosmology
The aim of this paper is to compute transitions amplitudes in quantum
cosmology, and in particular pair creation amplitudes and radiative
transitions. To this end, we apply a double adiabatic development to the
solutions of the Wheeler-DeWitt equation restricted to mini-superspace wherein
gravity is described by the scale factor . The first development consists in
working with instantaneous eigenstates, in , of the matter Hamiltonian. The
second development is applied to the gravitational part of the wave function
and generalizes the usual WKB approximation. We then obtain an exact equation
which replaces the Wheeler-DeWitt equation and determines the evolution, i.e.
the dependence in , of the coefficients of this double expansion. When
working in the gravitational adiabatic approximation, the simplified equation
delivers the unitary evolution of transition amplitudes occurring among
instantaneous eigenstates. Upon abandoning this approximation, one finds that
there is an additional coupling among matter states living in expanding and
contracting universes. Moreover one has to face also the Klein paradox, i.e.
the generation of backward waves from an initially forward wave. The
interpretation and the consequences of these unusual features are only sketched
in the present paper. Finally, the examples of pair creation and radiative
transitions are analyzed in detail to establish when and how the above
mentioned unitary evolution coincides with the Schr\" odinger evolution.Comment: 27 pages, Late
Time dependent Green functions from Wheeler De Witt solutions
The aim of this article is twofold. First we examine from a new angle the
question of recovery of time in quantum cosmology. We construct Green functions
for matter fields from the solutions of the Wheeler De Witt equation. For
simplicity we work in a mini-superspace context. By evaluating these Green
functions in a first order development of the energy ``increment'' induced by
matrix elements of field operators, we show that the background geometry is the
solution of Einstein equations driven by the mean matter energy and that it is
this background which determines the time lapses separating the field
operators. Then, by studying higher order corrections, we clarify the nature of
the small dimensionless parameters which guarantee the validity of the
approximations used. In this respect, we show that the formal expansion in the
inverse Planck mass which is sometime presented as the ``standard procedure''
is illegitimate. Secondly, by the present analysis of Green functions, we
prepare the study of quantum matter transitions in quantum cosmology. In a next
article, we show that the time parametrization of transition amplitudes appears
for the same reasons that it appeared in this article. This proves that the
background is dynamically determined by the transition under examination.Comment: 25 pages, latex, no figure
Notes on moving mirrors
The Davies-Fulling (DF) model describes the scattering of a massless field by
a non-inertial mirror in two dimensions. In this paper, we generalize this
model in two different ways. First, we consider partially reflecting mirrors.
We show that the Bogoliubov coefficients relating inertial modes can be
expressed in terms of the frequency dependent reflection factor which is
specified in the rest frame of the mirror and the transformation from the
inertial modes to the modes at rest with respect to the mirror. In this
perspective, the DF model is simply the limiting case when this factor is unity
for all frequencies. In the second part, we introduce an alternative model
which is based on self-interactions described by an action principle. When the
coupling is constant, this model can be solved exactly and gives rise to a
partially reflecting mirror. The usefulness of this dynamical model lies in the
possibility of switching off the coupling between the mirror and the field.
This allows to obtain regularized expressions for the fluxes in situations
where they are singular when using the DF model. Two examples are considered.
The first concerns the flux induced by the disappearance of the reflection
condition, a situation which bears some analogies with the end of the
evaporation of a black hole. The second case concerns the flux emitted by a
uniformly accelerated mirror.Comment: 27 pages and 2 figures LaTeX2
Confronting the trans-Planckian question of inflationary cosmology with dissipative effects
We provide a class of QFTs which exhibit dissipation above a threshold
energy, thereby breaking Lorentz invariance. Unitarity is preserved by coupling
the fields to additional degrees of freedom (heavy fields) which introduce the
rest frame. Using the Equivalence Principle, we define these theories in
arbitrary curved spacetime. We then confront the trans-Planckian question of
inflationary cosmology. When dissipation increases with the energy, the quantum
field describing adiabatic perturbations is completely damped at the onset of
inflation. However it still exists as a composite operator made with the
additional fields. And when these are in their ground state, the standard power
spectrum obtains if the threshold energy is much larger that the Hubble
parameter. In fact, as the energy redshifts below the threshold, the composite
operator behaves as if it were a free field endowed with standard vacuum
fluctuations. The relationship between our models and the Brane World scenarios
studied by Libanov and Rubakov displaying similar effects is discussed. The
signatures of dissipation will be studied in a forthcoming paper.Comment: 30 pages, 1 Figure, to appear in CQ
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