Harmonic oscillator with nonzero minimal uncertainties in both position and momentum in a SUSYQM framework

In the context of a two-parameter $(\alpha, \beta)$ 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 $\alpha$, $\beta$ vanishes, in which case shape invariance under parameter translation occurs. In the special case where $\alpha = \beta \ne 0$, the oscillator Hamiltonian is shown to coincide with that of the q-deformed oscillator with $q > 1$ and its eigenvectors are therefore $n$-$q$-boson states. In the general case where $0 \ne \alpha \ne \beta \ne 0$, the eigenvectors are constructed as linear combinations of $n$-$q$-boson states by resorting to a Bargmann representation of the latter and to $q$-differential calculus. They are finally expressed in terms of a $q$-exponential and little $q$-Jacobi polynomials.Comment: LaTeX, 24 pages, no figure, minor changes, additional references, final version to be published in JP

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 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 $\delta x \delta t > 0$, which vanishes in the limit of weak string coupling.Comment: 8 pages, LaTe

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

Lorentz-covariant deformed algebra with minimal length

The $D$-dimensional two-parameter deformed algebra with minimal length introduced by Kempf is generalized to a Lorentz-covariant algebra describing a ($D+1$)-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

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

Minimum Length Cutoff in Inflation and Uniqueness of the Action

According to most inflationary models, fluctuations that are of cosmological size today started out much smaller than any plausible cutoff length such as the string or Planck lengths. It has been shown that this could open an experimental window for testing models of the short-scale structure of space-time. The observability of effects hinges crucially, however, on the initial conditions imposed on the new comoving modes which are continually being created at the cutoff length scale. Here, we address this question while modelling spacetime as obeying the string and quantum gravity inspired minimum length uncertainty principle. We find that the usual strategy for determining the initial conditions faces an unexpected difficulty because it involves reformulating the action and discarding a boundary term: we find that actions that normally differ merely by a boundary term can differ significantly when the minimum length is introduced. This is possible because the introduction of a minimum length comes with an ordering ambiguity much like the ordering ambiguity that arises with the introduction of hbar in the process of quantization.Comment: 18 pages, 1 figur

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

Comparison of organic and conventional pig productions on prevalence, antibiotic resistance and genetic diversity of Escherichia coli

The objectives of this study were to assess the prevalence, the tetracycline resistance level and the genetic diversity of Escherichia coli isolated from organic pigs in comparison with conventional pigs. This study is integrated in a global European project, Safeorganic, funded trough CORE Organic II call. 25 organic and 25 conventional herds were considered in one slaughterhouse from April to October 2012. Colon content of 2 pigs per herds was sampled. For each pig, enumeration of E. coli and of tetracycline resistant E. coli (TET+E. coli) was determined