Orthogonality Relations and Supercharacter Formulas of U(m|n) Representations

In this paper we obtain the orthogonality relations for the supergroup U(m|n), which are remarkably different from the ones for the U(N) case. We extend our results for ordinary representations, obtained some time ago, to the case of complex conjugated and mixed representations. Our results are expressed in terms of the Young tableaux notation for irreducible representations. We use the supersymmetric Harish-Chandra-Itzykson-Zuber integral and the character expansion technique as mathematical tools for deriving these relations. As a byproduct we also obtain closed expressions for the supercharacters and dimensions of some particular irreducible U(m|n) representations. A new way of labeling the U(m|n) irreducible representations in terms of m + n numbers is proposed. Finally, as a corollary of our results, new identities among the dimensions of the irreducible representations of the unitary group U(N) are presented.Comment: 56 pages, LaTeX, changes only in the writing of the titl

Currents between tethered electrodes in a magnetized laboratory plasma

Laboratory experiments on important plasma physics issues of electrodynamic tethers were performed. These included current propagation, formation of wave wings, limits of current collection, nonlinear effects and instabilities, charging phenomena, and characteristics of transmission lines in plasmas. The experiments were conducted in a large afterglow plasma. The current system was established with a small electron-emitting hot cathode tethered to an electron-collecting anode, both movable across the magnetic field and energized by potential difference up to V approx.=100 T(sub e). The total current density in space and time was obtained from complete measurements of the perturbed magnetic field. The fast spacecraft motion was reproduced in the laboratory by moving the tethered electrodes in small increments, applying delayed current pulses, and reconstructing the net field by a linear superposition of locally emitted wavelets. With this technique, the small-amplitude dc current pattern is shown to form whistler wings at each electrode instead of the generally accepted Alfven wings. For the beam electrode, the whistler wing separates from the field-aligned beam which carries no net current. Large amplitude return currents to a stationary anode generate current-driven microinstabilities, parallel electric fields, ion depletions, current disruptions and time-varying electrode charging. At appropriately high potentials and neutral densities, excess neutrals are ionized near the anode. The anode sheath emits high-frequency electron transit-time oscillations at the sheath-plasma resonance. The beam generates Langmuir turbulence, ion sound turbulence, electron heating, space charge fields, and Hall currents. An insulated, perfectly conducting transmission line embedded in the plasma becomes lossy due to excitation of whistler waves and magnetic field diffusion effects. The implications of the laboratory observations on electrodynamic tethers in space are discussed

Host Galaxies of Young Dust-Reddened Quasars

We present results on a multiwavelength campaign to identify the nature of dust-reddened Type 1 quasars. These quasars were selected by matching FIRST, 2MASS and very red optical counterparts with r' − K > 5. We find a very high fraction of Low Ionization Broad Absorption Line Quasars (LoBALs) among AGN selected with this method, perhaps a sign of quasar feedback. From X-ray observations and Balmer decrement measurements, the obscuring dust is most likely located in a cold absorber such as the host galaxy, rather than from a torus near the AGN. Hubble ACS imaging of a sub-sample of these sources showed a very high fraction of interacting and merging systems. The quasars appear to be very young in which dust from the merging galaxies is still settling in. Spitzer IRS and MIPS data show star formation signatures and deep Silicate absorption features in these objects, but overall the quasar is the dominant source in the Mid-infrared

A Five Dimensional Perspective on Many Particles in the Snyder basis of Double Special Relativity

After a brief summary of Double Special Relativity (DSR), we concentrate on a five dimensional procedure, which consistently introduce coordinates and momenta in the corresponding four-dimensional phase space, via a Hamiltonian approach. For the one particle case, the starting point is a de Sitter momentum space in five dimensions, with an additional constraint selected to recover the mass shell condition in four dimensions. Different basis of DSR can be recovered by selecting specific gauges to define the reduced four dimensional degrees of freedom. This is shown for the Snyder basis in the one particle case. We generalize the method to the many particles case and apply it again to this basis. We show that the energy and momentum of the system, given by the dynamical variables that are generators of translations in space and time and which close the Poincar\'e algebra, are additive magnitudes. From this it results that the rest energy (mass) of a composite object does not have an upper limit, as opposed to a single component particle which does.Comment: 12 pages, no figures, AIP Conf. Pro

Duality for massive spin two theories in arbitrary dimensions

Using the parent Lagrangian approach we construct a dual formulation, in the sense originally proposed by Curtright and Freund, of a massive spin two Fierz-Pauli theory in arbitrary dimensions $D$. This is achieved in terms of a mixed symmetry tensor $T_{A[B_{1}B_{2}... B_{D-2}]}$, without the need of auxiliary fields. The relation of this method with an alternative formulation based on a gauge symmetry principle proposed by Zinoviev is elucidated. We show that the latter formulation in four dimensions, with a given gauge fixing together with a definite sequence of auxiliary fields elimination via their equations of motion, leads to the parent Lagrangian already considered by West completed by a Fierz-Pauli mass term, which in turns yields the Curtright-Freund action. This motivates our generalization to arbitrary dimensions leading to the corresponding extension of the four dimensional result. We identify the transverse true degrees of freedom of the dual theory and verify that their number is in accordance with those of the massive Fierz-Pauli field.Comment: 14 pages, no figures, revtex 4. Some new comments and explanations have been added and the notation homogeneize

Uncertainties in climate change projections and regional downscaling: implications for water resources management

Climate change is expected to have a large impact on water resources worldwide. A major problem in assessing the potential impact of a changing climate on these resources is the difference in spatial scale between available climate change projections and water resources management. Regional climate models (RCMs) are often used for the spatial disaggregation of the outputs of global circulation models. However, RCMs are time-intensive to run and typically only a small number of model runs is available for a certain region of interest. This paper investigates the value of the improved representation of local climate processes by a regional climate model for water resources management in the tropical Andes of Ecuador. This region has a complex hydrology and its water resources are under pressure. Compared to the IPCC AR4 model ensemble, the regional climate model PRECIS does indeed capture local gradients better than global models, but locally the model is prone to large discrepancies between observed and modelled precipitation. It is concluded that a further increase in resolution is necessary to represent local gradients properly. Furthermore, to assess the uncertainty in downscaling, an ensemble of regional climate models should be implemented. Finally, translating the climate variables to streamflow using a hydrological model constitutes a smaller but not negligible source of uncertainty

Emergent electrodynamics from the Nambu model for spontaneous Lorentz symmetry breaking

After imposing the Gauss law constraint as an initial condition upon the Hilbert space of the Nambu model, in all its generic realizations, we recover QED in the corresponding non-linear gauge A_{\mu}A^{\mu}=n^{2}M^{2}. Our result is non-perturbative in the parameter M for n^{2}\neq 0 and can be extended to the n^{2}=0 case. This shows that in the Nambu model, spontaneous Lorentz symmetry breaking dynamically generates gauge invariance, provided the Gauss law is imposed as an initial condition. In this way electrodynamics is recovered, with the photon being realized as the Nambu-Goldstone modes of the spontaneously broken symmetry, which finally turns out to be non-observableComment: 17 page

Highly charged ions: optical clocks and applications in fundamental physics

Recent developments in frequency metrology and optical clocks have been based on electronic transitions in atoms and singly charged ions as references. These systems have enabled relative frequency uncertainties at a level of a few parts in $10^{-18}$. This accomplishment not only allows for extremely accurate time and frequency measurements, but also to probe our understanding of fundamental physics, such as variation of fundamental constants, violation of the local Lorentz invariance, and forces beyond the Standard Model of Physics. In addition, novel clocks are driving the development of sophisticated technical applications. Crucial for applications of clocks in fundamental physics are a high sensitivity to effects beyond the Standard Model and Einstein's Theory of Relativity and a small frequency uncertainty of the clock. Highly charged ions offer both. They have been proposed as highly accurate clocks, since they possess optical transitions which can be extremely narrow and less sensitive to external perturbations compared to current atomic clock species. The selection of highly charged ions in different charge states offers narrow transitions that are among the most sensitive ones for a change in the fine-structure constant and the electron-to-proton mass ratio, as well as other new physics effects. Recent advances in trapping and sympathetic cooling of highly charged ions will in the future enable high accuracy optical spectroscopy. Progress in calculating the properties of selected highly charged ions has allowed the evaluation of systematic shifts and the prediction of the sensitivity to the "new physics" effects. This article reviews the current status of theory and experiment in the field.Comment: 53 pages, 16 figures, submitted to RM

A univariate estimation of the Philippine’s exchange rate

This study aims to forecast the Exchange Rate of the Philippines for five years starting from 2016 to 2020, and determine which among Inflation Rate, Purchasing Power of Peso, Interest Rate, Exports, Imports, and Balance of Payments is a significant factor that can influence Exchange Rate. The researchers used the monthly data of the variables starting from January 1999 to December 2015, which were gathered from Bangko Sentral ng Pilipinas with a total of 204 observations. In forecasting the dependent variable, the researchers used the Box-Jenkins Methodology. The researchers also examined the relationship between the variables using the Pairwise Granger Causality Testand Johansen Cointegration Test. Stepwise Multiple Linear Regression was also performed to determine the significant factors that can actually predict the Exchange Rate.Keywords: Box-Jenkins Methodology; Exchange Rate; Paired t-test; GrangerCausuality; Johansen Cointegration Test; Regression