462 research outputs found
Quanta Without Quantization
The dimensional properties of fields in classical general relativity lead to
a tangent tower structure which gives rise directly to quantum mechanical and
quantum field theory structures without quantization. We derive all of the
fundamental elements of quantum mechanics from the tangent tower structure,
including fundamental commutation relations, a Hilbert space of pure and mixed
states, measurable expectation values, Schroedinger time evolution, collapse of
a state and the probability interpretation. The most central elements of string
theory also follow, including an operator valued mode expansion like that in
string theory as well as the Virasoro algebra with central charges.Comment: 8 pages, Latex, Honorable Mention 1997 GRG Essa
A nonlinear quantum model of the Friedmann universe
A discussion is given of the quantisation of a physical system with finite
degrees of freedom subject to a Hamiltonian constraint by treating time as a
constrained classical variable interacting with an unconstrained quantum state.
This leads to a quantisation scheme that yields a Schrodinger-type equation
which is in general nonlinear in evolution. Nevertheless it is compatible with
a probabilistic interpretation of quantum mechanics and in particular the
construction of a Hilbert space with a Euclidean norm is possible. The new
scheme is applied to the quantisation of a Friedmann Universe with a massive
scalar field whose dynamical behaviour is investigated numerically.Comment: 11 pages of text + 4 pages for 8 figure
A controlled experiment for the empirical evaluation of safety analysis techniques for safety-critical software
Context: Today's safety critical systems are increasingly reliant on
software. Software becomes responsible for most of the critical functions of
systems. Many different safety analysis techniques have been developed to
identify hazards of systems. FTA and FMEA are most commonly used by safety
analysts. Recently, STPA has been proposed with the goal to better cope with
complex systems including software. Objective: This research aimed at comparing
quantitatively these three safety analysis techniques with regard to their
effectiveness, applicability, understandability, ease of use and efficiency in
identifying software safety requirements at the system level. Method: We
conducted a controlled experiment with 21 master and bachelor students applying
these three techniques to three safety-critical systems: train door control,
anti-lock braking and traffic collision and avoidance. Results: The results
showed that there is no statistically significant difference between these
techniques in terms of applicability, understandability and ease of use, but a
significant difference in terms of effectiveness and efficiency is obtained.
Conclusion: We conclude that STPA seems to be an effective method to identify
software safety requirements at the system level. In particular, STPA addresses
more different software safety requirements than the traditional techniques FTA
and FMEA, but STPA needs more time to carry out by safety analysts with little
or no prior experience.Comment: 10 pages, 1 figure in Proceedings of the 19th International
Conference on Evaluation and Assessment in Software Engineering (EASE '15).
ACM, 201
Field Theory as Free Fall
It is shown that the classical field equations pertaining to gravity coupled
to other bosonic fields are equivalent to a single geodesic equation,
describing the free fall of a point particle in superspace. Some implications
for quantum gravity are discussed.Comment: 18 pages, plain late
The large cosmological constant approximation to classical and quantum gravity: model examples
We have recently introduced an approach for studying perturbatively classical
and quantum canonical general relativity. The perturbative technique appears to
preserve many of the attractive features of the non-perturbative quantization
approach based on Ashtekar's new variables and spin networks. With this
approach one can find perturbatively classical observables (quantities that
have vanishing Poisson brackets with the constraints) and quantum states
(states that are annihilated by the quantum constraints). The relative ease
with which the technique appears to deal with these traditionally hard problems
opens several questions about how relevant the results produced can possibly
be. Among the questions is the issue of how useful are results for large values
of the cosmological constant and how the approach can deal with several
pathologies that are expected to be present in the canonical approach to
quantum gravity. With the aim of clarifying these points, and to make our
construction as explicit as possible, we study its application in several
simple models. We consider Bianchi cosmologies, the asymmetric top, the coupled
harmonic oscillators with constant energy density and a simple quantum
mechanical system with two Hamiltonian constraints. We find that the technique
satisfactorily deals with the pathologies of these models and offers promise
for finding (at least some) results even for small values of the cosmological
constant. Finally, we briefly sketch how the method would operate in the full
four dimensional quantum general relativity case.Comment: 21 pages, RevTex, 2 figures with epsfi
Semi-classical States, Effective Dynamics and Classical Emergence in Loop Quantum Cosmology
We construct physical semi-classical states annihilated by the Hamiltonian
constraint operator in the framework of loop quantum cosmology as a method of
systematically determining the regime and validity of the semi-classical limit
of the quantum theory. Our results indicate that the evolution can be
effectively described using continuous classical equations of motion with
non-perturbative corrections down to near the Planck scale below which the
universe can only be described by the discrete quantum constraint. These
results, for the first time, provide concrete evidence of the emergence of
classicality in loop quantum cosmology and also clearly demarcate the domain of
validity of different effective theories. We prove the validity of modified
Friedmann dynamics incorporating discrete quanum geometry effects which can
lead to various new phenomenological applications. Furthermore the
understanding of semi-classical states allows for a framework for interpreting
the quantum wavefunctions and understanding questions of a semi-classical
nature within the quantum theory of loop quantum cosmology.Comment: Accepted for publication in Phys Rev D. Updated version to matc
Free fields via canonical transformations of matter-coupled 2D dilaton gravity models
It is shown that the 1+1-dimensional matter-coupled Jackiw-Teitelboim model
and the model with an exponential potential can be converted by means of
appropriate canonical transformations into a bosonic string theory propagating
on a flat target space with an indefinite signature. This makes it possible to
consistently quantize these models in the functional Schroedinger
representation thus generalizing recent results on CGHS theory.Comment: 15 pages, Late
General relativity histories theory II: Invariance groups
We show in detail how the histories description of general relativity carries
representations of both the spacetime diffeomorphisms group and the Dirac
algebra of constraints. We show that the introduction of metric-dependent
equivariant foliations leads to the crucial result that the canonical
constraints are invariant under the action of spacetime diffeomorphisms.
Furthermore, there exists a representation of the group of generalised
spacetime mappings that are functionals of the four-metric: this is a spacetime
analogue of the group originally defined by Bergmann and Komar in the context
of the canonical formulation of general relativity. Finally, we discuss the
possible directions for the quantization of gravity in histories theory.Comment: 24 pages, submitted to Class. Quant. Gra
Polymer Parametrised Field Theory
Free scalar field theory on 2 dimensional flat spacetime, cast in
diffeomorphism invariant guise by treating the inertial coordinates of the
spacetime as dynamical variables, is quantized using LQG type `polymer'
representations for the matter field and the inertial variables. The quantum
constraints are solved via group averaging techniques and, analogous to the
case of spatial geometry in LQG, the smooth (flat) spacetime geometry is
replaced by a discrete quantum structure. An overcomplete set of Dirac
observables, consisting of (a) (exponentials of) the standard free scalar field
creation- annihilation modes and (b) canonical transformations corresponding to
conformal isometries, are represented as operators on the physical Hilbert
space. None of these constructions suffer from any of the `triangulation'
dependent choices which arise in treatments of LQG. In contrast to the standard
Fock quantization, the non- Fock nature of the representation ensures that the
algebra of conformal isometries as well as that of spacetime diffeomorphisms
are represented in an anomaly free manner. Semiclassical states can be analysed
at the gauge invariant level. It is shown that `physical weaves' necessarily
underly such states and that such states display semiclassicality with respect
to, at most, a countable subset of the (uncountably large) set of observables
of type (a). The model thus offers a fertile testing ground for proposed
definitions of quantum dynamics as well as semiclassical states in LQG.Comment: 44 pages, no figure
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