437 research outputs found
Macdonald Polynomials from Sklyanin Algebras: A Conceptual Basis for the -Adics-Quantum Group Connection
We establish a previously conjectured connection between -adics and
quantum groups. We find in Sklyanin's two parameter elliptic quantum algebra
and its generalizations, the conceptual basis for the Macdonald polynomials,
which ``interpolate'' between the zonal spherical functions of related real and
\--adic symmetric spaces. The elliptic quantum algebras underlie the
\--Baxter models. We show that in the n \air \infty limit, the Jost
function for the scattering of {\em first} level excitations in the
\--Baxter model coincides with the Harish\--Chandra\--like \--function
constructed from the Macdonald polynomials associated to the root system .
The partition function of the \--Baxter model itself is also expressed in
terms of this Macdonald\--Harish\--Chandra\ \--function, albeit in a less
simple way. We relate the two parameters and of the Macdonald
polynomials to the anisotropy and modular parameters of the Baxter model. In
particular the \--adic ``regimes'' in the Macdonald polynomials correspond
to a discrete sequence of XXZ models. We also discuss the possibility of
``\--deforming'' Euler products.Comment: 25 page
The role of matter density uncertainties in the analysis of future neutrino factory experiments
Matter density uncertainties can affect the measurements of the neutrino
oscillation parameters at future neutrino factory experiments, such as the
measurements of the mixing parameters and \deltacp. We compare
different matter density uncertainty models and discuss the possibility to
include the matter density uncertainties in a complete statistical analysis.
Furthermore, we systematically study in which measurements and where in the
parameter space matter density uncertainties are most relevant. We illustrate
this discussion with examples that show the effects as functions of different
magnitudes of the matter density uncertainties. We find that matter density
uncertainties are especially relevant for large \stheta \gtrsim 10^{-3}.
Within the KamLAND-allowed range, they are most relevant for the precision
measurements of \stheta and \deltacp, but less relevant for ``binary''
measurements, such as for the sign of \ldm, the sensitivity to \stheta, or
the sensitivity to maximal CP violation. In addition, we demonstrate that
knowing the matter density along a specific baseline better than to about 1%
precision means that all measurements will become almost independent of the
matter density uncertainties.Comment: 21 pages, 7 figures, LaTeX. Final version to be published in Phys.
Rev.
Integrable Structure of Conformal Field Theory, Quantum KdV Theory and Thermodynamic Bethe Ansatz
We construct the quantum versions of the monodromy matrices of KdV theory.
The traces of these quantum monodromy matrices, which will be called as ``-operators'', act in highest weight Virasoro modules. The -operators depend on the spectral parameter and their expansion
around generates an infinite set of commuting Hamiltonians
of the quantum KdV system. The -operators can be viewed as the
continuous field theory versions of the commuting transfer-matrices of
integrable lattice theory. In particular, we show that for the values
of the Virasoro central charge
the eigenvalues of the -operators satisfy a closed system of
functional equations sufficient for determining the spectrum. For the
ground-state eigenvalue these functional equations are equivalent to those of
massless Thermodynamic Bethe Ansatz for the minimal conformal field theory
; in general they provide a way to generalize the technique
of Thermodynamic Bethe Ansatz to the excited states. We discuss a
generalization of our approach to the cases of massive field theories obtained
by perturbing these Conformal Field Theories with the operator .
The relation of these -operators to the boundary states is also
briefly described.Comment: 24 page
Eureka and beyond: mining's impact on African urbanisation
This collection brings separate literatures on mining and urbanisation together at a time when both artisanal and large-scale mining are expanding in many African economies. While much has been written about contestation over land and mineral rights, the impact of mining on settlement, notably its catalytic and fluctuating effects on migration and urban growth, has been largely ignored. African nation-statesâ urbanisation trends have shown considerable variation over the past half century. The current surge in ânewâ mining countries and the slow-down in âoldâ mining countries are generating some remarkable settlement patterns and welfare outcomes. Presently, the African continent is a laboratory of national mining experiences. This special issue on African mining and urbanisation encompasses a wide cross-section of country case studies: beginning with the historical experiences of mining in Southern Africa (South Africa, Zambia, Zimbabwe), followed by more recent mineralizing trends in comparatively new mineral-producing countries (Tanzania) and an established West African gold producer (Ghana), before turning to the influence of conflict minerals (Angola, the Democratic Republic of Congo and Sierra Leone)
Age validation of juvenile Shortfin Mako (Isurus oxyrinchus) tagged and marked with oxytetracycline off southern California
The purpose of this study was to validate aging results of juvenile Shortfin Mako (Isurus oxyrinchus) by vertebral band counts. Vertebrae of 29 juvenile Shortfin Mako marked with oxytetracycline (OTC) were obtained from tag-recapture activities to determine centrum growth-band deposition. Tagging occurred off southern California from 1996 to 2010, and time at liberty of the 29 sharks ranged from 4 months to 4.4 years (mean=1.3 years). Growth information also was obtained from length-frequency modal analyses (MULTIFAN and MIXDIST) by using a 29-year data set of commercial and research catch data, in addition to a tag-recapture growth model (e.g, the GROTAG model). For vertebrae samples used for age validation, shark size at time of release ranged from 79 to 142 cm fork length (FL) and from 98 to 200 cm FL at recapture. Results from band counts of vertebrae distal to OTC marks indicate 2 band pairs (2 translucent and 2 opaque) are formed each year for Shortfin Mako of the size range examined. Length-frequency analyses identified 3 age class modes. Growth rate estimates from 26.5 to 35.5 cm/year were calculated for the first age-class mode (85 cm FL) and from 22.4 to 28.6 cm/year for the second age-class mode (130 cm FL). Results from the tag-recapture growth model revealed fast growth during time at liberty for tagged fish of the 2 youngest age classes. Collectively, these methods suggest rapid growth of juvenile Shortfin Mako in the southern California study area and indicate biannual deposition of growth bands in vertebrae for the first 5 years
Universally Coupled Massive Gravity, II: Densitized Tetrad and Cotetrad Theories
Einstein's equations in a tetrad formulation are derived from a linear theory
in flat spacetime with an asymmetric potential using free field gauge
invariance, local Lorentz invariance and universal coupling. The gravitational
potential can be either covariant or contravariant and of almost any density
weight. These results are adapted to produce universally coupled massive
variants of Einstein's equations, yielding two one-parameter families of
distinct theories with spin 2 and spin 0. The theories derived, upon fixing the
local Lorentz gauge freedom, are seen to be a subset of those found by
Ogievetsky and Polubarinov some time ago using a spin limitation principle. In
view of the stability question for massive gravities, the proven non-necessity
of positive energy for stability in applied mathematics in some contexts is
recalled. Massive tetrad gravities permit the mass of the spin 0 to be heavier
than that of the spin 2, as well as lighter than or equal to it, and so provide
phenomenological flexibility that might be of astrophysical or cosmological
use.Comment: 2 figures. Forthcoming in General Relativity and Gravitatio
Non-standard Hamiltonian effects on neutrino oscillations
We investigate non-standard Hamiltonian effects on neutrino oscillations,
which are effective additional contributions to the vacuum or matter
Hamiltonian. Since these effects can enter in either flavor or mass basis, we
develop an understanding of the difference between these bases representing the
underlying theoretical model. In particular, the simplest of these effects are
classified as ``pure'' flavor or mass effects, where the appearance of such a
``pure'' effect can be quite plausible as a leading non-standard contribution
from theoretical models. Compared to earlier studies investigating particular
effects, we aim for a top-down classification of a possible ``new physics''
signature at future long-baseline neutrino oscillation precision experiments.
We develop a general framework for such effects with two neutrino flavors and
discuss the extension to three neutrino flavors, as well as we demonstrate the
challenges for a neutrino factory to distinguish the theoretical origin of
these effects with a numerical example. We find how the precision measurement
of neutrino oscillation parameters can be altered by non-standard effects alone
(not including non-standard interactions in the creation and detection
processes) and that the non-standard effects on Hamiltonian level can be
distinguished from other non-standard effects (such as neutrino decoherence and
decay) if we consider specific imprint of the effects on the energy spectra of
several different oscillation channels at a neutrino factory.Comment: 30 pages, 6 figures, LaTeX, final version, published in Eur.Phys.J.
Supercoherent States, Super K\"ahler Geometry and Geometric Quantization
Generalized coherent states provide a means of connecting square integrable
representations of a semi-simple Lie group with the symplectic geometry of some
of its homogeneous spaces. In the first part of the present work this point of
view is extended to the supersymmetric context, through the study of the
OSp(2/2) coherent states. These are explicitly constructed starting from the
known abstract typical and atypical representations of osp(2/2). Their
underlying geometries turn out to be those of supersymplectic OSp(2/2)
homogeneous spaces. Moment maps identifying the latter with coadjoint orbits of
OSp(2/2) are exhibited via Berezin's symbols. When considered within
Rothstein's general paradigm, these results lead to a natural general
definition of a super K\"ahler supermanifold, the supergeometry of which is
determined in terms of the usual geometry of holomorphic Hermitian vector
bundles over K\"ahler manifolds. In particular, the supergeometry of the above
orbits is interpreted in terms of the geometry of Einstein-Hermitian vector
bundles. In the second part, an extension of the full geometric quantization
procedure is applied to the same coadjoint orbits. Thanks to the super K\"ahler
character of the latter, this procedure leads to explicit super unitary
irreducible representations of OSp(2/2) in super Hilbert spaces of
superholomorphic sections of prequantum bundles of the Kostant type. This work
lays the foundations of a program aimed at classifying Lie supergroups'
coadjoint orbits and their associated irreducible representations, ultimately
leading to harmonic superanalysis. For this purpose a set of consistent
conventions is exhibited.Comment: 53 pages, AMS-LaTeX (or LaTeX+AMSfonts
Gravitational excitons from extra dimensions
Inhomogeneous multidimensional cosmological models with a higher dimensional
space-time manifold are investigated under dimensional reduction. In the
Einstein conformal frame, small excitations of the scale factors of the
internal spaces near minima of an effective potential have a form of massive
scalar fields in the external space-time. Parameters of models which ensure
minima of the effective potentials are obtained for particular cases and masses
of gravitational excitons are estimated.Comment: Revised version --- 12 references added, Introduction enlarged, 20
pages, LaTeX, to appear in Phys.Rev.D56 (15.11.97
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