2,041 research outputs found
Groups of Fibonacci type revisited
This article concerns a class of groups of Fibonacci type introduced by Johnson and Mawdesley that includes Conway?s Fibonacci groups, the Sieradski groups, and the Gilbert-Howie groups. This class of groups provides an interesting focus for developing the theory of cyclically presented groups and, following questions by Bardakov and Vesnin and by Cavicchioli, Hegenbarth, and Repov?s, they have enjoyed renewed interest in recent years. We survey results concerning their algebraic properties, such as isomorphisms within the class, the classification of the finite groups, small cancellation properties, abelianizations, asphericity, connections with Labelled Oriented Graph groups, and the semigroups of Fibonacci type. Further, we present a new method of proving the classification of the finite groups that deals with all but three groups
Hamiltonian and physical Hilbert space in polymer quantum mechanics
In this paper, a version of polymer quantum mechanics, which is inspired by
loop quantum gravity, is considered and shown to be equivalent, in a precise
sense, to the standard, experimentally tested, Schroedinger quantum mechanics.
The kinematical cornerstone of our framework is the so called polymer
representation of the Heisenberg-Weyl (H-W) algebra, which is the starting
point of the construction. The dynamics is constructed as a continuum limit of
effective theories characterized by a scale, and requires a renormalization of
the inner product. The result is a physical Hilbert space in which the
continuum Hamiltonian can be represented and that is unitarily equivalent to
the Schroedinger representation of quantum mechanics. As a concrete
implementation of our formalism, the simple harmonic oscillator is fully
developed.Comment: 19 pages, 2 figures. Comments and references added. Version to be
published in CQ
Polymer state approximations of Schroedinger wave functions
It is shown how states of a quantum mechanical particle in the Schroedinger
representation can be approximated by states in the so-called polymer
representation. The result may shed some light on the semiclassical limit of
loop quantum gravity.Comment: 11 pages, 1 figure, Conclusions section adde
One-loop functions of a translation-invariant renormalizable noncommutative scalar model
Recently, a new type of renormalizable scalar model on
the Moyal space was proved to be perturbatively renormalizable. It is
translation-invariant and introduces in the action a term. We
calculate here the and functions at one-loop level for this
model. The coupling constant function is proved to have the
same behaviour as the one of the model on the commutative
. The function of the new parameter is also
calculated. Some interpretation of these results are done.Comment: 13 pages, 3 figure
Spectroscopy across the brown dwarf/planetary mass boundary - I. Near-infrared JHK spectra
With a uniform VLT SINFONI data set of nine targets, we have developed an
empirical grid of J,H,K spectra of the atmospheres of objects estimated to have
very low substellar masses of \sim5-20 MJup and young ages of \sim1-50 Myr.
Most of the targets are companions, objects which are especially valuable for
comparison with atmosphere and evolutionary models, as they present rare cases
in which the age is accurately known from the primary. Based on the sample
youth, all objects are expected to have low surface gravity, and this study
investigates the critical early phases of the evolution of substellar objects.
The spectra are compared with grids of five different theoretical atmosphere
models. This analysis represents the first systematic model comparison with
infrared spectra of young brown dwarfs. The fits to the full JHK spectra of
each object result in a range of best fit effective temperatures of +/-150-300K
whether or not the full model grid or a subset restricted to lower log(g)
values is used. This effective temperature range is significantly larger than
the uncertainty typically assigned when using a single model grid. Fits to a
single wavelength band can vary by up to 1000K using the different models.
Since the overall shape of these spectra is governed more by the temperature
than surface gravity, unconstrained model fits did not find matches with low
surface gravity or a trend in log(g) with age. This suggests that empirical
comparison with spectra of unambiguously young objects targets (such as these
SINFONI data) may be the most reliable method to search for indications of low
surface gravity and youth. For two targets, the SINFONI data are a second epoch
and the data show no variations in morphology over time. The analysis of two
other targets, AB Pic B and CT Cha B, suggests that these objects may have
lower temperatures, and consequently lower masses, than previously estimated.Comment: 15 pages, 13 figure
Commutative limit of a renormalizable noncommutative model
Renormalizable models on Moyal space have been obtained by
modifying the commutative propagator. But these models have a divergent "naive"
commutative limit. We explain here how to obtain a coherent such commutative
limit for a recently proposed translation-invariant model. The mechanism relies
on the analysis of the uv/ir mixing in general Feynman graphs.Comment: 11 pages, 3 figures, minor misprints being correcte
On The Interaction Of D0-Brane Bound States And RR Photons
We consider the problem of the interaction between D0-brane bound state and
1-form RR photons by the world-line theory. Based on the fact that in the
world-line theory the RR gauge fields depend on the matrix coordinates of
D0-branes, the gauge fields also appear as matrices in the formulation. At the
classical level, we derive the Lorentz-like equations of motion for D0-branes,
and it is observed that the center-of-mass is colourless with respect to the
SU(N) sector of the background. Using the path integral method, the
perturbation theory for the interaction between the bound state and the RR
background is developed. We discuss what kind of field theory may be
corresponded to the amplitudes which are calculated by the perturbation
expansion in world-line theory. Qualitative considerations show that the
possibility of existence of a map between the world-line theory and the
non-Abelian gauge theory is very considerable.Comment: LaTeX, 28 pages, 4 eps figures. v2 and v3: eqs. (3.18) and (B.2) are
corrected, very small change
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