167 research outputs found
Dust as a Standard of Space and Time in Canonical Quantum Gravity
The coupling of the metric to an incoherent dust introduces into spacetime a
privileged dynamical reference frame and time foliation. The comoving
coordinates of the dust particles and the proper time along the dust worldlines
become canonical coordinates in the phase space of the system. The Hamiltonian
constraint can be resolved with respect to the momentum that is canonically
conjugate to the dust time. Imposition of the resolved constraint as an
operator restriction on the quantum states yields a functional Schr\"{o}dinger
equation. The ensuing Hamiltonian density has an extraordinary feature: it
depends only on the geometric variables, not on the dust coordinates or time.
This has three important consequences. First, the functional Schr\"{o}dinger
equation can be solved by separating the dust time from the geometric
variables. Second, the Hamiltonian densities strongly commute and therefore can
be simultaneously defined by spectral analysis. Third, the standard constraint
system of vacuum gravity is cast into a form in which it generates a true Lie
algebra. The particles of dust introduce into space a privileged system of
coordinates that allows the supermomentum constraint to be solved explicitly.
The Schr\"{o}dinger equation yields a conserved inner product that can be
written in terms of either the instantaneous state functionals or the solutions
of constraints. Examples of gravitational observables are given, though neither
the intrinsic metric nor the extrinsic curvature are observables. Disregarding
factor--ordering difficulties, the introduction of dust provides a satisfactory
phenomenological approach to the problem of time in canonical quantum gravity.Comment: 56 pages (REVTEX file + 3 postscipt figure files
Dirac Constraint Quantization of a Dilatonic Model of Gravitational Collapse
We present an anomaly-free Dirac constraint quantization of the
string-inspired dilatonic gravity (the CGHS model) in an open 2-dimensional
spacetime. We show that the quantum theory has the same degrees of freedom as
the classical theory; namely, all the modes of the scalar field on an auxiliary
flat background, supplemented by a single additional variable corresponding to
the primordial component of the black hole mass. The functional Heisenberg
equations of motion for these dynamical variables and their canonical
conjugates are linear, and they have exactly the same form as the corresponding
classical equations. A canonical transformation brings us back to the physical
geometry and induces its quantization.Comment: 37 pages, LATEX, no figures, submitted to Physical Review
Application Perspective on Cybersecurity Testbed for Industrial Control Systems
The low-power wide-area (LPWA) technologies, which enable cost and energy-efficient wireless connectivity for massive deployments of autonomous machines, have enabled and boosted the development of many new Internet of things (IoT) applications; however, the security of LPWA technologies in general, and specifically those operating in the license-free frequency bands, have received somewhat limited attention so far. This paper focuses specifically on the security and privacy aspects of one of the most popular license-free-band LPWA technologies, which is named LoRaWAN. The paper’s key contributions are the details of the design and experimental validation of a security-focused testbed, based on the combination of software-defined radio (SDR) and GNU Radio software with a standalone LoRaWAN transceiver. By implementing the two practical man-in-the-middle attacks (i.e., the replay and bit-flipping attacks through intercepting the over-the-air activation procedure by an external to the network attacker device), we demonstrate that the developed testbed enables practical experiments for on-air security in real-life conditions. This makes the designed testbed perspective for validating the novel security solutions and approaches and draws attention to some of the relevant security challenges extant in LoRaWAN
Geometrodynamics of Schwarzschild Black Holes
The curvature coordinates of a Schwarz\-schild spacetime are turned
into canonical coordinates on the phase space of spherically
symmetric black holes. The entire dynamical content of the Hamiltonian theory
is reduced to the constraints requiring that the momenta vanish. What remains is a conjugate pair of canonical variables and
whose values are the same on every embedding. The coordinate is the
Schwarzschild mass, and the momentum the difference of parametrization
times at right and left infinities. The Dirac constraint quantization in the
new representation leads to the state functional which describes an unchanging superposition of black holes with different
masses. The new canonical variables may be employed in the study of collapsing
matter systems.Comment: 44 pages, Latex file, UU-REL-94/3/
Null dust in canonical gravity
We present the Lagrangian and Hamiltonian framework which incorporates null
dust as a source into canonical gravity. Null dust is a generalized Lagrangian
system which is described by six Clebsch potentials of its four-velocity Pfaff
form. The Dirac--ADM decomposition splits these into three canonical
coordinates (the comoving coordinates of the dust) and their conjugate momenta
(appropriate projections of four-velocity). Unlike ordinary dust of massive
particles, null dust therefore has three rather than four degrees of freedom
per space point. These are evolved by a Hamiltonian which is a linear
combination of energy and momentum densities of the dust. The energy density is
the norm of the momentum density with respect to the spatial metric. The
coupling to geometry is achieved by adding these densities to the gravitational
super-Hamiltonian and supermomentum. This leads to appropriate Hamiltonian and
momentum constraints in the phase space of the system. The constraints can be
rewritten in two alternative forms in which they generate a true Lie algebra.
The Dirac constraint quantization of the system is formally accomplished by
imposing the new constraints as quantum operator restrictions on state
functionals. We compare the canonical schemes for null and ordinary dust and
emhasize their differences.Comment: 25 pages, REVTEX, no figure
Discrete and continuum third quantization of Gravity
We give a brief introduction to matrix models and the group field theory
(GFT) formalism as realizations of the idea of a third quantization of gravity,
and present in some more detail the idea and basic features of a continuum
third quantization formalism in terms of a field theory on the space of
connections, building up on the results of loop quantum gravity that allow to
make the idea slightly more concrete. We explore to what extent one can
rigorously define such a field theory. Concrete examples are given for the
simple case of Riemannian GR in 3 spacetime dimensions. We discuss the relation
between GFT and this formal continuum third quantized gravity, and what it can
teach us about the continuum limit of GFTs.Comment: 21 pages, 5 eps figures; submitted as a contribution to the
proceedings of the conference "Quantum Field Theory and Gravity Conference
Regensburg 2010" (28 September - 1 October 2010, Regensburg/Bavaria); v2:
preprint number include
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