1,517 research outputs found
Harmonic oscillator with nonzero minimal uncertainties in both position and momentum in a SUSYQM framework
In the context of a two-parameter deformation of the
canonical commutation relation leading to nonzero minimal uncertainties in both
position and momentum, the harmonic oscillator spectrum and eigenvectors are
determined by using techniques of supersymmetric quantum mechanics combined
with shape invariance under parameter scaling. The resulting supersymmetric
partner Hamiltonians correspond to different masses and frequencies. The
exponential spectrum is proved to reduce to a previously found quadratic
spectrum whenever one of the parameters , vanishes, in which
case shape invariance under parameter translation occurs. In the special case
where , the oscillator Hamiltonian is shown to coincide
with that of the q-deformed oscillator with and its eigenvectors are
therefore --boson states. In the general case where , the eigenvectors are constructed as linear combinations of
--boson states by resorting to a Bargmann representation of the latter
and to -differential calculus. They are finally expressed in terms of a
-exponential and little -Jacobi polynomials.Comment: LaTeX, 24 pages, no figure, minor changes, additional references,
final version to be published in JP
On the Space-Time Uncertainty Relations of Liouville Strings and D Branes
Within a Liouville approach to non-critical string theory, we argue for a
non-trivial commutation relation between space and time observables, leading to
a non-zero space-time uncertainty relation , which
vanishes in the limit of weak string coupling.Comment: 8 pages, LaTe
The Effects of Fluorides on the Teeth
Mention was made, in the previous paper, of the fact that mottled enamel of the teeth results from the presence of fluorine in the water supply. The water of the city of Ankeny and surrounding territory may have a fluorine concentration to exceed eight or ten parts per million of water; mottled enamel is very prevalent in that area. Work by Smith (1) of the University of Arizona indicates that mottled enamel may result when the concentration of fluorine is as low as 0.8 to 0.9 part per million of water. The work of Schulz and Lamb (2) and McCollum, Simmonds, Becker, and Bunting (3) has demonstrated that sodium fluoride when fed to rats will produce abnormalities of the teeth of these animals similar to that generally known as mottled enamel in human beings. The work reported in this paper had as its object to ascertain if other inorganic fluorides will produce mottled enamel and also to determine if mottled enamel can be produced by organic fluorides. Furthermore, it was deemed advisable to ascertain if the administration of alum (aluminum sulphate) along with sodium fluoride would prevent the development of mottled enamel
The Influence of Sodium Fluoride upon the Composition of Tibiae of Rats Partially Recovering from Rickets
McClure (1) has recently called attention to the need for additional information dealing with the localization of fluorine in teeth and bones and with associative factors invoked in its absorption and metabolism. The work of Roholm (2) and Shortt (3) with the human being appeared to support this viewpoint strongly. Roholm (2) found that fluoride may cause either osteomalacia or osteosclerosis and that storage of fluorine in the bodies of female workers in the cryolite industry in Denmark was sometimes sufficiently great that, even after they left the factory, enough fluorine to cause tooth damage was secreted in their milk. Shortt (3) et al. found ostcosclerosis associated with 30 to 45 years residence in a mottled enamel area in India
On the spin of gravitational bosons
We unearth spacetime structure of massive vector bosons, gravitinos, and
gravitons. While the curvatures associated with these particles carry a
definite spin, the underlying potentials cannot be, and should not be,
interpreted as single spin objects. For instance, we predict that a spin
measurement in the rest frame of a massive gravitino will yield the result 3/2
with probability one half, and 1/2 with probability one half. The simplest
scenario leaves the Riemannian curvature unaltered; thus avoiding conflicts
with classical tests of the theory of general relativity. However, the quantum
structure acquires additional contributions to the propagators, and it gives
rise to additional phases.Comment: Honorable mention, 2002 Gravity Research Foundation Essay
Lorentz-covariant deformed algebra with minimal length
The -dimensional two-parameter deformed algebra with minimal length
introduced by Kempf is generalized to a Lorentz-covariant algebra describing a
()-dimensional quantized space-time. For D=3, it includes Snyder algebra
as a special case. The deformed Poincar\'e transformations leaving the algebra
invariant are identified. Uncertainty relations are studied. In the case of D=1
and one nonvanishing parameter, the bound-state energy spectrum and
wavefunctions of the Dirac oscillator are exactly obtained.Comment: 8 pages, no figure, presented at XV International Colloquium on
Integrable Systems and Quantum Symmetries (ISQS-15), Prague, June 15-17, 200
Mode Generating Mechanism in Inflation with Cutoff
In most inflationary models, space-time inflated to the extent that modes of
cosmological size originated as modes of wavelengths at least several orders of
magnitude smaller than the Planck length. Recent studies confirmed that,
therefore, inflationary predictions for the cosmic microwave background
perturbations are generally sensitive to what is assumed about the Planck
scale. Here, we propose a framework for field theories on curved backgrounds
with a plausible type of ultraviolet cutoff. We find an explicit mechanism by
which during cosmic expansion new (comoving) modes are generated continuously.
Our results allow the numerical calculation of a prediction for the CMB
perturbation spectrum.Comment: 9 pages, LaTe
On Signatures of Short Distance Physics in the Cosmic Microwave Background
Following a self-contained review of the basics of the theory of cosmological
perturbations, we discuss why the conclusions reached in the recent paper by
Kaloper et al are too pessimistic estimates of the amplitude of possible
imprints of trans-Planckian (string) physics on the spectrum of cosmic
microwave anisotropies in an inflationary Universe. It is shown that the likely
origin of large trans-Planckian effects on late time cosmological fluctuations
comes from nonadiabatic evolution of the state of fluctuations while the
wavelength is smaller than the Planck (string) scale, resulting in an excited
state at the time that the wavelength crosses the Hubble radius during
inflation.Comment: 11 pages, 4 figure
Asymptotically maximal families of hypersurfaces in toric varieties
A real algebraic variety is maximal (with respect to the Smith-Thom
inequality) if the sum of the Betti numbers (with coefficients)
of the real part of the variety is equal to the sum of Betti numbers of its
complex part. We prove that there exist polytopes that are not Newton polytopes
of any maximal hypersurface in the corresponding toric variety. On the other
hand we show that for any polytope there are families of hypersurfaces
with the Newton polytopes that are
asymptotically maximal when tends to infinity. We also show that
these results generalize to complete intersections.Comment: 18 pages, 1 figur
WKB approximation in deformed space with minimal length
The WKB approximation for deformed space with minimal length is considered.
The Bohr-Sommerfeld quantization rule is obtained. A new interesting feature in
presence of deformation is that the WKB approximation is valid for intermediate
quantum numbers and can be invalid for small as well as very large quantum
numbers. The correctness of the rule is verified by comparing obtained results
with exact expressions for corresponding spectra.Comment: 13 pages Now it is avaible at http://stacks.iop.org/0305-4470/39/37
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