Wedges, Cones, Cosmic Strings, and the Reality of Vacuum Energy

One of J. Stuart Dowker's most significant achievements has been to observe that the theory of diffraction by wedges developed a century ago by Sommerfeld and others provided the key to solving two problems of great interest in general-relativistic quantum field theory during the last quarter of the twentieth century: the vacuum energy associated with an infinitely thin, straight cosmic string, and (after an interchange of time with a space coordinate) the apparent vacuum energy of empty space as viewed by an accelerating observer. In a sense the string problem is more elementary than the wedge, since Sommerfeld's technique was to relate the wedge problem to that of a conical manifold by the method of images. Indeed, Minkowski space, as well as all cone and wedge problems, are related by images to an infinitely sheeted master manifold, which we call Dowker space. We review the research in this area and exhibit in detail the vacuum expectation values of the energy density and pressure of a scalar field in Dowker space and the cone and wedge spaces that result from it. We point out that the (vanishing) vacuum energy of Minkowski space results, from the point of view of Dowker space, from the quantization of angular modes, in precisely the way that the Casimir energy of a toroidal closed universe results from the quantization of Fourier modes; we hope that this understanding dispels any lingering doubts about the reality of cosmological vacuum energy.Comment: 28 pages, 16 figures. Special volume in honor of J. S. Dowke

Design and Development of Personal GeoServices for Universities

Personal GeoServices are emerging as an interaction paradigm linking users to information rich environments like a university campus or to Big Data sources like the Internet of Things by delivering spatially intelligent web-services. OpenStreetMap (OSM) constitutes a valuable source of spatial base-data that can be extracted, integrated, and utilised with such heterogeneous data sources for free. In this paper, we present a Personal GeoServices application built on OSM spatial data and university-specific business data for staff, faculty, and students. While generic products such as Google Maps and Google Earth enable basic forms of spatial exploration, the domain of a university campus presents specific business information needs, such as “What classes are scheduled in that room over there?” and “How can I get to Prof. Murray’s office from here?” Within the framework of the StratAG project (www.StratAG.ie), an eCampus Demonstrator was developed for the National University of Ireland Maynooth (NUIM) to assist university users in exploring and analysing their surroundings within a detailed data environment. This work describes this system in detail, discussing the usage of OSM vector data, and providing insights for developers of spatial information systems for personalised visual exploration of an area

Crossing Symmetry Violation of Unitarized Pion-Pion Amplitude in the Resonance Region

Pion-pion scattering amplitude obtained from one-loop Chiral Perturbation Theory (ChPT) is crossing symmetric, however the corresponding partial wave amplitudes do not respect exact unitarity relation. There are different approaches to get unitarized partial wave amplitudes from ChPT. Here we consider the inverse amplitude method (IAM) that is often used to fit pion-pion phase shifts to experimental data, by adjusting free parameters. We measure the amount of crossing symmetry violation (CSV) in this case and we show that crossing symmetry is badly violated by the IAM unitarized ChPT amplitude in the resonance region. Important CSV also occurs when all free parameters are set equal to zero.Comment: 6 pages, 4 figure

Hybrid squeezing of solitonic resonant radiation in photonic crystal fibers

We report on the existence of a novel kind of squeezing in photonic crystal fibers which is conceptually intermediate between the four-wave mixing induced squeezing, in which all the participant waves are monochromatic waves, and the self-phase modulation induced squeezing for a single pulse in a coherent state. This hybrid squeezing occurs when an arbitrary short soliton emits quasi-monochromatic resonant radiation near a zero group velocity dispersion point of the fiber. Photons around the resonant frequency become strongly correlated due to the presence of the classical soliton, and a reduction of the quantum noise below the shot noise level is predicted.Comment: 5 pages, 2 figure

Some Case Example Exact Solutions for Quadratically Nonlinear Optical Media with PT-Symmetric Potentials

In the present paper we consider an optical system with a χ (2)-type nonlinearity and unspecified PT -symmetric potential functions. Considering this as an inverse problem and positing a family of exact solutions in terms of cnoidal functions, we solve for the resulting potential functions in a way that ensures the potentials obey the requirements of PT -symmetry. We then focus on case examples of soliton and periodic solutions for which we present a stability analysis as a function of their amplitude parameters. Finally, we numerically explore the nonlinear dynamics of the associated waveforms to identify the outcome of the relevant dynamical instabilities of localized and extended states

Wavelength-Orthogonal Stiffening of Hydrogel Networks with Visible Light

Herein, we introduce the wavelength-orthogonal crosslinking of hydrogel networks using two red-shifted chromophores, i.e. acrylpyerene (AP, λ$_{activation}$=410–490 nm) and styrylpyrido[2,3-b]pyrazine (SPP, λ$_{activation}$=400–550 nm), able to undergo [2+2] photocycloaddition in the visible-light regime. The photoreactivity of the SPP moiety is pH-dependent, whereby an acidic environment inhibits the cycloaddition. By employing a spiropyran-based photoacid generator with suitable absorption wavelength, we are able to restrict the activation wavelength of the SPP moiety to the green light region (λ$_{activation}$=520–550 nm), enabling wavelength-orthogonal activation of the AP group. Our wavelength-orthogonal photochemical system was successfully applied in the design of hydrogels whose stiffness can be tuned independently by either green or blue light

Unitarized pion-nucleon scattering within Heavy Baryon Chiral Perturbation Theory

By means of the Inverse Amplitude Method we unitarize the elastic pion-nucleon scattering amplitudes obtained from Heavy Baryon Chiral Perturbation Theory to O(q^3). Within this approach we can enlarge their applicability range and generate the Delta(1232) resonance. We can find a reasonable description of the pion nucleon phase shifts with (q^2) parameters in agreement with the resonance saturation hypothesis. However, the uncertainties in the analysis of the low energy data as well as the large number of chiral parameters, which can have strong correlations, allow us to obtain very good fits with rather different sets of chiral constants.Comment: Shortened version to appear in Phys. Rev. D. Brief Report

K_S\rightarrow \gamma\gamma , K_L\rightarrow\pi^0\gamma\gamma$ and Unitarity

Agreement between the experimental value $\Gamma (K_S\rightarrow \gamma\gamma)$ and the number predicted via a one-loop chiral perturbation theory calculation has been cited as a success for the latter. On the other hand the one-loop prediction for the closely related process $K_L\rightarrow \pi^0\gamma\gamma$ has been found to be a factor three below the experimental value. Using the inputs of unitarity and dispersion relations, we demonstrate the importance of higher order loop effects to both of these processes.Comment: 20 pages (4 figures available on request), UMHEP-39