8,614 research outputs found
Unitary dynamics of spherical null gravitating shells
The dynamics of a thin spherically symmetric shell of zero-rest-mass matter
in its own gravitational field is studied. A form of action principle is used
that enables the reformulation of the dynamics as motion on a fixed background
manifold. A self-adjoint extension of the Hamiltonian is obtained via the group
quantization method. Operators of position and of direction of motion are
constructed. The shell is shown to avoid the singularity, to bounce and to
re-expand to that asymptotic region from which it contracted; the dynamics is,
therefore, truly unitary. If a wave packet is sufficiently narrow and/or
energetic then an essential part of it can be concentrated under its
Schwarzschild radius near the bounce point but no black hole forms. The quantum
Schwarzschild horizon is a linear combination of a black and white hole
apparent horizons rather than an event horizon.Comment: 26 pages, Latex, no figures; definitive version, to be published in
Nuclear Physics
Group quantization of parametrized systems I. Time levels
A method of quantizing parametrized systems is developed that is based on a
kind of ``gauge invariant'' quantities---the so-called perennials (a perennial
must also be an ``integral of motion''). The problem of time in its particular
form (frozen time formalism, global problem of time, multiple choice problem)
is met, as well as the related difficulty characteristic for this type of
theory: the paucity of perennials. The present paper is an attempt to find some
remedy in the ideas on ``forms of relativistic dynamics'' by Dirac. Some
aspects of Dirac's theory are generalized to all finite-dimensional first-class
parametrized systems. The generalization is based on replacing the Poicar\'{e}
group and the algebra of its generators as used by Dirac by a canonical group
of symmetries and by an algebra of elementary perennials. A number of insights
is gained; the following are the main results. First, conditions are revealed
under which the time evolution of the ordinary quantum mechanics, or a
generalization of it, can be constructed. The construction uses a kind of gauge
and time choice and it is described in detail. Second, the theory is structured
so that the quantum mechanics resulting from different choices of gauge and
time are compatible. Third, a practical way is presented of how a broad class
of problems can be solved without the knowledge of explicit form of perennials.Comment: After discussions at Imperial College, a great improvement is
achieved. I particular, it is shown that many problems can be solved without
explicit knowledge of the perennial
A critical look at strings
This is an invited contribution to the Special Issue of "Foundations of
Physics" titled "Forty Years Of String Theory: Reflecting On the Foundations".
I have been asked to assess string theory as an outsider, and to compare it
with the theory, methods, and expectations in my own field.Comment: 7 page
Relational evolution of the degrees of freedom of generally covariant quantum theories
We study the classical and quantum dynamics of generally covariant theories
with vanishing a Hamiltonian and with a finite number of degrees of freedom. In
particular, the geometric meaning of the full solution of the relational
evolution of the degrees of freedom is displayed, which means the determination
of the total number of evolving constants of motion required. Also a method to
find evolving constants is proposed. The generalized Heinsenberg picture needs
M time variables, as opposed to the Heisenberg picture of standard quantum
mechanics where one time variable t is enough. As an application, we study the
parameterized harmonic oscillator and the SL(2,R) model with one physical
degree of freedom that mimics the constraint structure of general relativity
where a Schrodinger equation emerges in its quantum dynamics.Comment: 25 pages, no figures, Latex file. Revised versio
The complete LQG propagator: II. Asymptotic behavior of the vertex
In a previous article we have show that there are difficulties in obtaining
the correct graviton propagator from the loop-quantum-gravity dynamics defined
by the Barrett-Crane vertex amplitude. Here we show that a vertex amplitude
that depends nontrivially on the intertwiners can yield the correct propagator.
We give an explicit example of asymptotic behavior of a vertex amplitude that
gives the correct full graviton propagator in the large distance limit.Comment: 16 page
SL(2,R) model with two Hamiltonian constraints
We describe a simple dynamical model characterized by the presence of two
noncommuting Hamiltonian constraints. This feature mimics the constraint
structure of general relativity, where there is one Hamiltonian constraint
associated with each space point. We solve the classical and quantum dynamics
of the model, which turns out to be governed by an SL(2,R) gauge symmetry,
local in time. In classical theory, we solve the equations of motion, find a
SO(2,2) algebra of Dirac observables, find the gauge transformations for the
Lagrangian and canonical variables and for the Lagrange multipliers. In quantum
theory, we find the physical states, the quantum observables, and the physical
inner product, which is determined by the reality conditions. In addition, we
construct the classical and quantum evolving constants of the system. The model
illustrates how to describe physical gauge-invariant relative evolution when
coordinate time evolution is a gauge.Comment: 9 pages, 1 figure, revised version, to appear in Phys. Rev.
Shortcomings of the Big Bounce derivation in Loop Quantum Cosmology
We give a prescription to define in Loop Quantum Gravity the electric field
operator related to the scale factor of an homogeneous and isotropic
cosmological space-time. This procedure allows to link the fundamental theory
with its cosmological implementation. In view of the conjugate relation
existing between holonomies and fluxes, the edge length and the area of
surfaces in the fiducial metric satisfy a duality condition. As a consequence,
the area operator has a discrete spectrum also in Loop Quantum Cosmology. This
feature makes the super-Hamiltonian regularization an open issue of the whole
formulation.Comment: 4 pages, accepted for publication in Phys. Rev. D as a Rapid
Communicatio
OUTLINE OF A GENERALLY COVARIANT QUANTUM FIELD THEORY AND A QUANTUM THEORY OF GRAVITY
We study a tentative generally covariant quantum field theory, denoted the
T-Theory, as a tool to investigate the consistency of quantum general
relativity. The theory describes the gravitational field and a minimally
coupled scalar field; it is based on the loop representation, and on a certain
number of quantization choices. Four-dimensional diffeomorphism-invariant
quantum transition probabilities can be computed from the theory. We present
the explicit calculation of the transition probability between two volume
eigenstates as an example. We discuss the choices on which the T-theory relies,
and the possibilities of modifying them.Comment: Latex file, 33 page
What simplified models say about unitarity and gravitational collapse
This paper is an extended version of a talk at the conference Constrained
Dynamics and Quantum Gravity QG99. It reviews some work on the quantum collapse
of the spherically symmetric gravitating thin shell of zero rest mass. Recent
results on Kucha\v{r} decomposition are applied. The constructed version of
quantum mechanics is unitary, although the shell falls under its Schwarzschild
radius if its energy is high enough. Rather that a permanent black hole,
something like a transient black and white hole pair seems to be created in
such a case.Comment: 17 pages, uses amstex, no figure
Hybrid mean field and real space model for vacancy diffusion-mediated annealing of radiation defects
In a fusion or advanced fission reactor, high energy neutrons induce the
formation of extended defect clusters in structural component materials,
degrading their properties over time. Such damage can be partially recovered
via a thermal annealing treatment. Therefore, for the design and operation of
fusion and advanced fission nuclear energy systems it is critical to estimate
and predict the annealing timescales for arbitrary configurations of defect
clusters. In our earlier paper [I. Rovelli, S. L. Dudarev, and A. P. Sutton, J.
Mech. Phys. Solids 103, 121 (2017)] we extended the Green function formulation
by Gu, Xiang et al. [Y. Gu, Y. Xiang, S. S. Quek, and D. J. Srolovitz, J. Mech.
Phys. Solids 83, 319 (2015)] for the climb of curved dislocations, to include
the evaporation and growth of cavities and vacancy clusters, and take into
account the effect of free surfaces. In this work, we further develop this
model to include the effect of radiation defects that are below the
experimental detection limit, via a mean field approach coupled with an
explicit treatment of the evolution of discrete defect clusters distributed in
real space. We show that randomly distributed small defects screen diffusive
interactions between larger discrete clusters. The evolution of the coupled
system is modelled self-consistently. We also simulate the evolution of defects
in an infinite laterally extended thin film, using the Ewald summation of
screened Yukawa-type diffusive propagators
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