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

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 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 $D$-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 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

Quantum Error Correction of Observables

A formalism for quantum error correction based on operator algebras was introduced in [1] via consideration of the Heisenberg picture for quantum dynamics. The resulting theory allows for the correction of hybrid quantum-classical information and does not require an encoded state to be entirely in one of the corresponding subspaces or subsystems. Here, we provide detailed proofs for the results of [1], derive a number of new results, and we elucidate key points with expanded discussions. We also present several examples and indicate how the theory can be extended to operator spaces and general positive operator-valued measures.Comment: 22 pages, 1 figure, preprint versio

Trans-Planckian Physics and the Spectrum of Fluctuations in a Bouncing Universe

In this paper, we calculate the spectrum of scalar field fluctuations in a bouncing, asymptotically flat Universe, and investigate the dependence of the result on changes in the physics on length scales shorter than the Planck length which are introduced via modifications of the dispersion relation. In this model, there are no ambiguities concerning the choice of the initial vacuum state. We study an example in which the final spectrum of fluctuations depends sensitively on the modifications of the dispersion relation without needing to invoke complex frequencies. Changes in the amplitude and in the spectral index are possible, in addition to modulations of the spectrum. This strengthens the conclusions of previous work in which the spectrum of cosmological perturbations in expanding inflationary cosmologies was studied, and it was found that, for dispersion relations for which the evolution is not adiabatic, the spectrum changes from the standard prediction of scale-invariance.Comment: 10 pages, 6 figures, RevTeX4. Analytical determination of the spectrum, corrected some typos, conclusions unchange

The Corley-Jacobson dispersion relation and trans-Planckian inflation

In this Letter we study the dependence of the spectrum of fluctuations in inflationary cosmology on possible effects of trans-Planckian physics, using the Corley/Jacobson dispersion relations as an example. We compare the methods used in previous work [1] with the WKB approximation, give a new exact analytical result, and study the dependence of the spectrum obtained using the approximate method of Ref. [1] on the choice of the matching time between different time intervals. We also comment on recent work subsequent to Ref. [1] on the trans-Planckian problem for inflationary cosmology.Comment: 6 pages, Revtex

Horizon Problem Remediation via Deformed Phase Space

We investigate the effects of a special kind of dynamical deformation between the momenta of the scalar field of the Brans-Dicke theory and the scale factor of the FRW metric. This special choice of deformation includes linearly a deformation parameter. We trace the deformation footprints in the cosmological equations of motion when the BD coupling parameter goes to infinity. One class of the solutions gives a constant scale factor in the late time that confirms the previous result obtained via another approach in the literature. This effect can be interpreted as a quantum gravity footprint in the coarse grained explanation. The another class of the solutions removes the big bang singularity, and the accelerating expansion region has an infinite temporal range which overcomes the horizon problem. After this epoch, there is a graceful exiting by which the universe enters in the radiation dominated era.Comment: 13 pages, 2 figures, to appear in GER

Novel approaches for the serodiagnosis of louse-borne relapsing fever

Louse-borne relapsing fever (LBRF) caused by B. recurrentis is a poverty-related and neglected infectious disease with an endemic focus in the Horn of Africa. Re-emergence of the disease occurred in Europe during the refugee crisis in 2015 and sporadic outbreaks were frequently reported in Eastern Africa where poor settings lack affordable diagnostics. Currently, there are no validated in vitro assays available for the serodiagnosis of LBRF. The aim of this study was to develop novel and reliable immunoassays by investigating clinically suspected and culture-confirmed serum samples from LBRF patients and a broad panel of serum samples from patients with other spirochetal, bacterial, and parasitic diseases. We identified two immunoreactive antigens (complement-inhibiting protein CihC and the glycerophosphodiester phosphodiesterase GlpQ of B. recurrentis) as the most promising target candidates leading to the evaluation of two immunoassays (line immunoblot and ELISA) for IgM and IgG. To optimize the IgM immunoassay, we conducted a bioinformatic approach to localize the relevant immunogenic regions within CihC. By utilizing a N-terminal CihC fragment, the sensitivity and specificity of both immunoassays (CihC and GlpQ) were high (IgM: sensitivity 100%, specificity of 89.9%, IgG: sensitivity 100%, specificity 99.2%). In conclusion, our findings indicate the diagnostic potential of CihC and GlpQ as valuable markers for the serodiagnosis of LBRF even at early time points of infection. Here, we provide strong evidence for the utilization of these immunoassays as reliable tools in clinical practice