Krein Spaces in de Sitter Quantum Theories

Experimental evidences and theoretical motivations lead to consider the curved space-time relativity based on the de Sitter group SO0(1,4) or Sp(2,2) as an appealing substitute to the flat space-time Poincaré relativity. Quantum elementary systems are then associated to unitary irreducible representations of that simple Lie group. At the lowest limit of the discrete series lies a remarkable family of scalar representations involving Krein structures and related undecomposable representation cohomology which deserves to be thoroughly studied in view of quantization of the corresponding carrier fields. The purpose of this note is to present the mathematical material needed to examine the problem and to indicate possible extensions of an exemplary case, namely the so-called de Sitterian massless minimally coupled field, i.e. a scalar field in de Sitter space-time which does not couple to the Ricci curvature

Pelagic metabolism of the Scheldt estuary measured by the oxygen method on an annual scale

Pelagic gross primary production (GPP), community respiration (CR) and nitrification were measured in the turbid Scheldt Estuary by the oxygen Winkler method from January to December 2003 at monthly intervals (EUROTROPH EU project). Five stations along the estuary were investigated, corresponding to a salinity (S) range of 0-25. Water was sampled and incubated until sunset in 60 ml glass bottles stored in a 5 compartment incubator kept at in situ temperature by flowing water. Irradiance was controlled in each compartment by filters having a shading capacity ranging from 0 to 100%. In order to estimate the oxygen consumption due to the respiration and nitrification processes, samples were incubated, in the dark compartment, with and without addition of nitrification inhibitors. Net community production (NCP) was most of the time negative in the estuary with values ranging from -275 to +31mmol O2.m-2.d-1 and the lowest values were found near Antwerp (S = 2). Strong pelagic GPP and positive NCP rates were observed in the freshwater part during summer with a maximal value in June (+373mmol O2.m-2.d-1), corresponding to an increase of the O2 concentration and a decrease of the partial pressure of CO2 (pCO2) in the water column during this period. Nitrification contributes 5 to 60% of the oxygen consumption in the water column with highest values measured in the inner part of the estuary due to high ammonium and suspended matter concentrations. Assuming a C/O2 molar ratio of 0.07, we estimated that nitrification represents on an annual scale 35% of organic matter production at salinity 2 which is consistent with previous estimates. NCP rates measured in 2003 are among the lowest reported in the literature and confirm the strong heterotrophic status of the Scheldt Estuary

Gazeau-Klauder type coherent states for hypergeometric type operators

The hypergeometric type operators are shape invariant, and a factorization into a product of first order differential operators can be explicitly described in the general case. Some additional shape invariant operators depending on several parameters are defined in a natural way by starting from this general factorization. The mathematical properties of the eigenfunctions and eigenvalues of the operators thus obtained depend on the values of the involved parameters. We study the parameter dependence of orthogonality, square integrability and of the monotony of eigenvalue sequence. The obtained results allow us to define certain systems of Gazeau-Klauder coherent states and to describe some of their properties. Our systematic study recovers a number of well-known results in a natural unified way and also leads to new findings.Comment: An error occurring in Theorem 12 and Theorem 13 has been correcte

Dissipation in ferrofluids: Mesoscopic versus hydrodynamic theory

Part of the field dependent dissipation in ferrofluids occurs due to the rotational motion of the ferromagnetic grains relative to the viscous flow of the carrier fluid. The classical theoretical description due to Shliomis uses a mesoscopic treatment of the particle motion to derive a relaxation equation for the non-equilibrium part of the magnetization. Complementary, the hydrodynamic approach of Liu involves only macroscopic quantities and results in dissipative Maxwell equations for the magnetic fields in the ferrofluid. Different stress tensors and constitutive equations lead to deviating theoretical predictions in those situations, where the magnetic relaxation processes cannot be considered instantaneous on the hydrodynamic time scale. We quantify these differences for two situations of experimental relevance namely a resting fluid in an oscillating oblique field and the damping of parametrically excited surface waves. The possibilities of an experimental differentiation between the two theoretical approaches is discussed.Comment: 14 pages, 2 figures, to appear in PR

Power Spectrum in Krein Space Quantization

The power spectrum of scalar field and space-time metric perturbations produced in the process of inflation of universe, have been presented in this paper by an alternative approach to field quantization namely, Krein space quantization [1,2]. Auxiliary negative norm states, the modes of which do not interact with the physical world, have been utilized in this method. Presence of negative norm states play the role of an automatic renormalization device for the theory.Comment: 8 pages, appear in Int. J. Theor. Phy

Whole-system metabolism and CO₂ fluxes in a Mediterranean Bay dominated by seagrass beds (Palma Bay, NW Mediterranean)

The relationship between whole-system metabolism estimates based on planktonic and benthic incubations (bare sediments and seagrass, Posidonia oceanica meadows), and CO2 fluxes across the air-sea interface were examined in the Bay of Palma (Mallorca, Spain) during two cruises in March and June 2002. Moreover, planktonic and benthic incubations were performed at monthly intervals from March 2001 to October 2002 in a seagrass vegetated area of the bay. From the annual study, results showed a contrast between the planktonic compartment, which was heterotrophic during most of the year, except for occasional bloom episodes, and the benthic compartment, which was slightly autotrophic. Whereas the seagrass community was autotrophic, the excess organic carbon production therein could only balance the excess respiration of the planktonic compartment in shallow waters (<10 m) relative to the maximum depth of the bay (55 m). This generated a horizontal gradient from autotrophic or balanced communities in the shallow, seagrass-covered areas of the bay, to strongly heterotrophic communities in deeper areas, consistent with the patterns of CO2 fields and fluxes across the bay observed during the two extensive cruises in 2002. Finally, dissolved inorganic carbon and oxygen budgets provided NEP estimates in fair agreement with those derived from direct metabolic estimates based on incubated samples over the Posidonia oceanica meadow

Stress tensor fluctuations in de Sitter spacetime

The two-point function of the stress tensor operator of a quantum field in de Sitter spacetime is calculated for an arbitrary number of dimensions. We assume the field to be in the Bunch-Davies vacuum, and formulate our calculation in terms of de Sitter-invariant bitensors. Explicit results for free minimally coupled scalar fields with arbitrary mass are provided. We find long-range stress tensor correlations for sufficiently light fields (with mass m much smaller than the Hubble scale H), namely, the two-point function decays at large separations like an inverse power of the physical distance with an exponent proportional to m^2/H^2. In contrast, we show that for the massless case it decays at large separations like the fourth power of the physical distance. There is thus a discontinuity in the massless limit. As a byproduct of our work, we present a novel and simple geometric interpretation of de Sitter-invariant bitensors for pairs of points which cannot be connected by geodesics.Comment: 35 pages, 4 figure

Conformal linear gravity in de Sitter space II

From the group theoretical point of view, it is proved that the theory of linear conformal gravity should be written in terms of a tensor field of rank-3 and mixed symmetry [Binegar, et al, Phys. Rev. D 27, (1983) 2249]. We obtained such a field equation in de Sitter space [Takook, et al, J. Math. Phys. 51, (2010) 032503]. In this paper, a proper solution to this equation is obtained as a product of a generalized polarization tensor and a massless scalar field and then the conformally invariant two-point function is calculated. This two-point function is de Sitter invariant and free of any pathological large-distance behavior.Comment: 16 pages, no figure, published versio

Semiclassical and quantum description of motion on noncommutative plane

We study the canonical and the coherent state quantization of a particle moving in a magnetic field on a non-commutative plane. Starting from the so called \theta-modified action, we perform the canonical quantization and analyze the gauge dependence of the obtained quantum theory. We construct the Malkin-Man'ko coherent states of the system in question, and the corresponding quantization. On this base, we study the relation between the coherent states and the "classical" trajectories predicted by the \theta-modified action. In addition, we construct different semiclassical states, making use of special properties of circular squeezed states. With the help of these states, we perform the Berezin-Klauder-Toeplitz quantization and present a numerical exploration of the semiclassical behavior of physical quantities in these states.Comment: 20 page

Artificial neural network analysis of factors controling ecosystem metabolism in coastal systems

Knowing the metabolic balance of an ecosystem is of utmost importance in determining whether the system is a net source or net sink of carbon dioxide to the atmosphere. However, obtaining these estimates often demands significant amounts of time and manpower. Here we present a simplified way to obtain an estimation of ecosystem metabolism. We used artificial neural networks (ANNs) to develop a mathematical model of the gross primary production to community respiration ratio (GPP:CR) based on input variables derived from three widely contrasting European coastal ecosystems (Scheldt Estuary, Randers Fjord, and Bay of Palma). Although very large gradients of nutrient concentration, light penetration, and organic-matter concentration exist across the sites, the factors that best predict the GPP:CR ratio are sampling depth, dissolved organic carbon (DOC) concentration, and temperature. We propose that, at least in coastal ecosystems, metabolic balance can be predicted relatively easily from these three predictive factors. An important conclusion of this work is that ANNs can provide a robust tool for the determination of ecosystem metabolism in coastal ecosystems