Reconstructing the geometric structure of a Riemannian symmetric space from its Satake diagram

The local geometry of a Riemannian symmetric space is described completely by the Riemannian metric and the Riemannian curvature tensor of the space. In the present article I describe how to compute these tensors for any Riemannian symmetric space from the Satake diagram, in a way that is suited for the use with computer algebra systems. As an example application, the totally geodesic submanifolds of the Riemannian symmetric space SU(3)/SO(3) are classified. The submission also contains an example implementation of the algorithms and formulas of the paper as a package for Maple 10, the technical documentation for this implementation, and a worksheet carrying out the computations for the space SU(3)/SO(3) used in the proof of Proposition 6.1 of the paper.Comment: 23 pages, also contains two Maple worksheets and technical documentatio

Greenhouse gas intensity of an irrigated cropping system in Saskatchewan

Non-Peer ReviewedIn response to increasing global food demands, the proportion of irrigated agricultural land within the Canadian Prairies is likely to increase. However, the implications of this with respect to the agricultural greenhouse gas (GHG) balance are not well understood. This study investigates and compares the greenhouse gas intensity of a typical irrigated and dryland cropping system in Saskatchewan, a semi-arid region of the Canadian Prairies. Compared to their dryland counterpart, irrigated cropping systems have higher GHG emissions which are a result of the energy used for pumping and larger nitrous oxide (N2O) production rates associated with higher N-fertilizer application and moist soil conditions. These emissions may be partially offset by increased carbon sequestration from the greater productivity realized through irrigation. This investigation focuses on the quantification of soil GHG emissions through chamber-based flux measurements. Factors driving these emissions have been determined through in-situ soil temperature, matric potential, and moisture measurements. The emissions associated with pumping and other crop management activities are accounted for using the Intergovernmental Panel on Climate Change (IPCC) literature and methodology. Preliminary results from the first season of study confirm that irrigated cropping systems have greater greenhouse gas intensity. Soil N2O emissions from the irrigated system were four times greater than the dryland and were the greatest source of emissions for the irrigated system. Diesel combustion used to power equipment was comparable between cropping systems. Emissions associated with pumping were notable; however, due to the wet growing season they remained smaller than could be expected most years. The information derived from this study will aid in the development of regional specific soil emission factors, improved management strategies, and will identify new approaches for mitigating emissions

Warped metrics for location-scale models

This paper argues that a class of Riemannian metrics, called warped metrics, plays a fundamental role in statistical problems involving location-scale models. The paper reports three new results : i) the Rao-Fisher metric of any location-scale model is a warped metric, provided that this model satisfies a natural invariance condition, ii) the analytic expression of the sectional curvature of this metric, iii) the exact analytic solution of the geodesic equation of this metric. The paper applies these new results to several examples of interest, where it shows that warped metrics turn location-scale models into complete Riemannian manifolds of negative sectional curvature. This is a very suitable situation for developing algorithms which solve problems of classification and on-line estimation. Thus, by revealing the connection between warped metrics and location-scale models, the present paper paves the way to the introduction of new efficient statistical algorithms.Comment: preprint of a submission to GSI 2017 conferenc

Effective QCD Partition Function in Sectors with Non-Zero Topological Charge and Itzykson-Zuber Type Integral

It was conjectured by Jackson et.al. that the finite volume effective partition function of QCD with the topological charge $M-N$ coincides with the Itzyskon-Zuber type integral for $M\times N$ rectangular matrices. In the present article we give a proof of this conjecture, in which the original Itzykson-Zuber integral is utilized.Comment: 7pages, LaTeX2

Structure and magnetic properties of the cubic oxide fluoride BaFeO2F

Fluorination of the parent oxide, BaFeO3- δ, with polyvinylidine fluoride gives rise to a cubic compound with a = 4.0603(4) Å at 298K. 57Fe Mössbauer spectra confirmed that all the iron is present as Fe3+. Neutron diffraction data showed complete occupancy of the anion sites indicating a composition BaFeO2F, with a large displacement of the iron off-site. The magnetic ordering temperature was determined as TN = 645±5K. Neutron diffraction data at 4.2K established G-type antiferromagnetism with a magnetic moment per Fe3+ ion of 3.95μB. However, magnetisation measurements indicated the presence of a weak ferromagnetic moment which is assigned to the canting of the antiferromagnetic structure. 57Fe Mössbauer spectra in the temperature range 10 to 300K were fitted with a model of fluoride ion distribution that retains charge neutrality of the perovskite unit cel

A few remarks on integral representation for zonal spherical functions on the symmetric space SU(N)/SO(N,R)SU(N)/SO(N,\R)

The integral representation on the orthogonal groups for zonal spherical functions on the symmetric space $SU(N)/SO(N,\R)$ is used to obtain a generating function for such functions. For the case N=3 the three-dimensional integral representation reduces to a one-dimensional one.Comment: Latex file, 10 pages, amssymb.sty require

Quantum Mechanics on SO(3) via Non-commutative Dual Variables

We formulate quantum mechanics on SO(3) using a non-commutative dual space representation for the quantum states, inspired by recent work in quantum gravity. The new non-commutative variables have a clear connection to the corresponding classical variables, and our analysis confirms them as the natural phase space variables, both mathematically and physically. In particular, we derive the first order (Hamiltonian) path integral in terms of the non-commutative variables, as a formulation of the transition amplitudes alternative to that based on harmonic analysis. We find that the non-trivial phase space structure gives naturally rise to quantum corrections to the action for which we find a closed expression. We then study both the semi-classical approximation of the first order path integral and the example of a free particle on SO(3). On the basis of these results, we comment on the relevance of similar structures and methods for more complicated theories with group-based configuration spaces, such as Loop Quantum Gravity and Spin Foam models.Comment: 29 pages; matches the published version plus footnote 7, a journal reference include

Generalized quantum tomographic maps

Some non-linear generalizations of classical Radon tomography were recently introduced by M. Asorey et al [Phys. Rev. A 77, 042115 (2008), where the straight lines of the standard Radon map are replaced by quadratic curves (ellipses, hyperbolas, circles) or quadratic surfaces (ellipsoids, hyperboloids, spheres). We consider here the quantum version of this novel non-linear approach and obtain, by systematic use of the Weyl map, a tomographic encoding approach to quantum states. Non-linear quantum tomograms admit a simple formulation within the framework of the star-product quantization scheme and the reconstruction formulae of the density operators are explicitly given in a closed form, with an explicit construction of quantizers and dequantizers. The role of symmetry groups behind the generalized tomographic maps is analyzed in some detail. We also introduce new generalizations of the standard singular dequantizers of the symplectic tomographic schemes, where the Dirac delta-distributions of operator-valued arguments are replaced by smooth window functions, giving rise to the new concept of "thick" quantum tomography. Applications for quantum state measurements of photons and matter waves are discussed.Comment: 8 page

Symplectically-invariant soliton equations from non-stretching geometric curve flows

A moving frame formulation of geometric non-stretching flows of curves in the Riemannian symmetric spaces $Sp(n+1)/Sp(1)\times Sp(n)$ and $SU(2n)/Sp(n)$ is used to derive two bi-Hamiltonian hierarchies of symplectically-invariant soliton equations. As main results, multi-component versions of the sine-Gordon (SG) equation and the modified Korteweg-de Vries (mKdV) equation exhibiting $Sp(1)\times Sp(n-1)$ invariance are obtained along with their bi-Hamiltonian integrability structure consisting of a shared hierarchy of symmetries and conservation laws generated by a hereditary recursion operator. The corresponding geometric curve flows in $Sp(n+1)/Sp(1)\times Sp(n)$ and $SU(2n)/Sp(n)$ are shown to be described by a non-stretching wave map and a mKdV analog of a non-stretching Schr\"odinger map.Comment: 39 pages; remarks added on algebraic aspects of the moving frame used in the constructio

Charge Orbits of Extremal Black Holes in Five Dimensional Supergravity

We derive the U-duality charge orbits, as well as the related moduli spaces, of "large" and "small" extremal black holes in non-maximal ungauged Maxwell-Einstein supergravities with symmetric scalar manifolds in d=5 space-time dimensions. The stabilizer groups of the various classes of orbits are obtained by determining and solving suitable U-invariant sets of constraints, both in "bare" and "dressed" charges bases, with various methods. After a general treatment of attractors in real special geometry (also considering non-symmetric cases), the N=2 "magic" theories, as well as the N=2 Jordan symmetric sequence, are analyzed in detail. Finally, the half-maximal (N=4) matter-coupled supergravity is also studied in this context.Comment: 1+63 pages, 6 Table