9,859 research outputs found
New Operators for Spin Net Gravity: Definitions and Consequences
Two operators for quantum gravity, angle and quasilocal energy, are briefly
reviewed. The requirements to model semi-classical angles are discussed. To
model semi-classical angles it is shown that the internal spins of the vertex
must be very large, ~10^20.Comment: 7 pages, 2 figures, a talk at the MG9 Meeting, Rome, July 2-8, 200
Operators for quantized directions
Inspired by the spin geometry theorem, two operators are defined which
measure angles in the quantum theory of geometry. One operator assigns a
discrete angle to every pair of surfaces passing through a single vertex of a
spin network. This operator, which is effectively the cosine of an angle, is
defined via a scalar product density operator and the area operator. The second
operator assigns an angle to two ``bundles'' of edges incident to a single
vertex. While somewhat more complicated than the earlier geometric operators,
there are a number of properties that are investigated including the full
spectrum of several operators and, using results of the spin geometry theorem,
conditions to ensure that semiclassical geometry states replicate classical
angles.Comment: v1: 20 pages, 23 figures v2: changes in presentation and
regularization (final results unchanged). This is an expanded version of the
one to be published in Class. Quant. Gra
Quantum Geometry Phenomenology: Angle and Semiclassical States
The phenomenology for the deep spatial geometry of loop quantum gravity is
discussed. In the context of a simple model of an atom of space, it is shown
how purely combinatorial structures can affect observations. The angle operator
is used to develop a model of angular corrections to local, continuum
flat-space 3-geometries. The physical effects involve neither breaking of local
Lorentz invariance nor Planck scale suppression, but rather reply on only the
combinatorics of SU(2) recouping theory. Bhabha scattering is discussed as an
example of how the effects might be observationally accessible.Comment: 5 pages, slightly extended version of the contribution to the
Loops'11 conference proceeding
A Spin Network Primer
Spin networks, essentially labeled graphs, are ``good quantum numbers'' for
the quantum theory of geometry. These structures encompass a diverse range of
techniques which may be used in the quantum mechanics of finite dimensional
systems, gauge theory, and knot theory. Though accessible to undergraduates,
spin network techniques are buried in more complicated formulations. In this
paper a diagrammatic method, simple but rich, is introduced through an
association of 2 by 2 matrices to diagrams. This spin network diagrammatic
method offers new perspectives on the quantum mechanics of angular momentum,
group theory, knot theory, and even quantum geometry. Examples in each of these
areas are discussed.Comment: A review of spin networks suitable for students of advanced quantum
mechanics (undergraduate). 16 pages, many eps figures, to be published in Am.
J. Phys v2: Updated to include key referenc
Does listening to a personal music player or reading a book during the uptake period of a PET-CT oncology scan cause extra 18F-fluorodeoxyglucose (18FDG) activity in the skeletal muscles?
Peer reviewe
Analysis of standing vertical jumps using a force platform
A force platform analysis of vertical jumping provides an engaging demonstration of the kinematics and dynamics of one-dimensional motion. The height of the jump may be calculated (1) from the flight time of the jump, (2) by applying the impulse–momentum theorem to the force–time curve, and (3) by applying the work–energy theorem to the force-displacement curve
The Snowmelt-Runoff Model (SRM) user's manual
A manual to provide a means by which a user may apply the snowmelt runoff model (SRM) unaided is presented. Model structure, conditions of application, and data requirements, including remote sensing, are described. Guidance is given for determining various model variables and parameters. Possible sources of error are discussed and conversion of snowmelt runoff model (SRM) from the simulation mode to the operational forecasting mode is explained. A computer program is presented for running SRM is easily adaptable to most systems used by water resources agencies
The three-dimensional carrier-envelope-phase map of focused few-cycle pulsed Gaussian beams
We derive an analytical expression that describes the complete
three-dimensional carrier-envelope phase (CEP) distribution of in the focal
volume of ultrashort pulsed Gaussian beams focused by spherical mirrors or
lenses. The focal CEP map depends on the so-called factor specifying the
frequency-dependence of the beam width of the source few-cycle pulse, on its
chirp and on the small chromatic aberration introduced by a lens without
appreciably distorting or broadening the few-cycle pulse. We show how to tailor
the CEP map of mirror-focused and lens-focused few-cycle pulses in order to
produce negligible transversal and axial CEP variations in specific regions of
the focal volume for phase-sensitive interactions of light with matter taking
place in a volume or on a surface. We propose a quasi-achromatic doublet lens
that can implement in practice these tailored CEP distributions.Comment: 9 pages, 6 figure
On the Universality of the Entropy-Area Relation
We present an argument that, for a large class of possible dynamics, a
canonical quantization of gravity will satisfy the Bekenstein-Hawking
entropy-area relation. This result holds for temperatures low compared to the
Planck temperature and for boundaries with areas large compared to Planck area.
We also relate our description, in terms of a grand canonical ensemble, to
previous geometric entropy calculations using area ensembles.Comment: 6 page
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