First results for the Coulomb gauge integrals using NDIM

The Coulomb gauge has at least two advantages over other gauge choices in that bound states between quarks and studies of confinement are easier to understand in this gauge. However, perturbative calculations, namely Feynman loop integrations, are not well defined (there are the so-called energy integrals) even within the context of dimensional regularization. Leibbrandt and Williams proposed a possible cure to such a problem by splitting the space-time dimension into D = ω + ρ, i.e., introducing a specific parameter ρ to regulate the energy integrals. The aim of our work is to apply the negative dimensional integration method (NDIM) to the Coulomb gauge integrals using the recipe of split-dimension parameters and present complete results - finite and divergent parts - to the one- and two-loop level for arbitrary exponents of the propagators and dimension.

Evaluating residues and integrals through negative dimensional integration method (NDIM)

The standard way of evaluating residues and some real integrals through the residue theorem (Cauchy's theorem) is well-known and widely applied in many branches of Physics. Herein we present an alternative technique based on the negative dimensional integration method (NDIM) originally developed to handle Feynman integrals. The advantage of this new technique is that we need only to apply Gaussian integration and solve systems of linear algebraic equations, with no need to determine the poles themselves or their residues, as well as obtaining a whole class of results for differing orders of poles simultaneously.

Coordenadas vestidas: formulação segundo a interpretação de Dirac-Feynman para a mecânica quântica e aplicações em CQED

Pós-graduação em Física - IFT

Use of computer algebra in the calculation of Feynman diagrams

The increasing precision of current and future experiments in high-energy physics requires a likewise increase in the accuracy of the calculation of theoretical predictions, in order to find evidence for possible deviations of the generally accepted Standard Model of elementary particles and interactions. Calculating the experimentally measurable cross sections of scattering and decay processes to a higher accuracy directly translates into including higher order radiative corrections in the calculation. The large number of particles and interactions in the full Standard Model results in an exponentially growing number of Feynman diagrams contributing to any given process in higher orders. Additionally, the appearance of multiple independent mass scales makes even the calculation of single diagrams non-trivial. For over two decades now, the only way to cope with these issues has been to rely on the assistance of computers. The aim of the xloops project is to provide the necessary tools to automate the calculation procedures as far as possible, including the generation of the contributing diagrams and the evaluation of the resulting Feynman integrals. The latter is based on the techniques developed in Mainz for solving one- and two-loop diagrams in a general and systematic way using parallel/orthogonal space methods. These techniques involve a considerable amount of symbolic computations. During the development of xloops it was found that conventional computer algebra systems were not a suitable implementation environment. For this reason, a new system called GiNaC has been created, which allows the development of large-scale symbolic applications in an object-oriented fashion within the C++ programming language. This system, which is now also in use for other projects besides xloops, is the main focus of this thesis. The implementation of GiNaC as a C++ library sets it apart from other algebraic systems. Our results prove that a highly efficient symbolic manipulator can be designed in an object-oriented way, and that having a very fine granularity of objects is also feasible. The xloops-related parts of this work consist of a new implementation, based on GiNaC, of functions for calculating one-loop Feynman integrals that already existed in the original xloops program, as well as the addition of supplementary modules belonging to the interface between the library of integral functions and the diagram generator.

Automatisierte Berechnung von Feynman-Graphen

Die Berechnung von experimentell überprüfbaren Vorhersagen aus dem Standardmodell mit Hilfe störungstheoretischer Methoden ist schwierig. Die Herausforderungen liegen in der Berechnung immer komplizierterer Feynman-Integrale und dem zunehmenden Umfang der Rechnungen für Streuprozesse mit vielen Teilchen. Neue mathematische Methoden müssen daher entwickelt und die zunehmende Komplexität durch eine Automatisierung der Berechnungen gezähmt werden. In Kapitel 2 wird eine kurze Einführung in diese Thematik gegeben. Die nachfolgenden Kapitel sind dann einzelnen Beiträgen zur Lösung dieser Probleme gewidmet. In Kapitel 3 stellen wir ein Projekt vor, das für die Analysen der LHC-Daten wichtig sein wird. Ziel des Projekts ist die Berechnung von Einschleifen-Korrekturen zu Prozessen mit vielen Teilchen im Endzustand. Das numerische Verfahren wird dargestellt und erklärt. Es verwendet Helizitätsspinoren und darauf aufbauend eine neue Tensorreduktionsmethode, die Probleme mit inversen Gram-Determinanten weitgehend vermeidet. Es wurde ein Computerprogramm entwickelt, das die Berechnungen automatisiert ausführen kann. Die Implementierung wird beschrieben und Details über die Optimierung und Verifizierung präsentiert. Mit analytischen Methoden beschäftigt sich das vierte Kapitel. Darin wird das xloopsnosp-Projekt vorgestellt, das verschiedene Feynman-Integrale mit beliebigen Massen und Impulskonfigurationen analytisch berechnen kann. Die wesentlichen mathematischen Methoden, die xloops zur Lösung der Integrale verwendet, werden erklärt. Zwei Ideen für neue Berechnungsverfahren werden präsentiert, die sich mit diesen Methoden realisieren lassen. Das ist zum einen die einheitliche Berechnung von Einschleifen-N-Punkt-Integralen, und zum anderen die automatisierte Reihenentwicklung von Integrallösungen in höhere Potenzen des dimensionalen Regularisierungsparameters $epsilon$. Zum letzteren Verfahren werden erste Ergebnisse vorgestellt. Die Nützlichkeit der automatisierten Reihenentwicklung aus Kapitel 4 hängt von der numerischen Auswertbarkeit der Entwicklungskoeffizienten ab. Die Koeffizienten sind im allgemeinen Multiple Polylogarithmen. In Kapitel 5 wird ein Verfahren für deren numerische Auswertung vorgestellt. Dieses neue Verfahren für Multiple Polylogarithmen wurde zusammen mit bekannten Verfahren für andere Polylogarithmus-Funktionen als Bestandteil der CC-Bibliothek ginac implementiert.

Continuum tensor network field states, path integral representations and spatial symmetries

A natural way to generalize tensor network variational classes to quantum field systems is via a continuous tensor contraction. This approach is first illustrated for the class of quantum field states known as continuous matrix-product states (cMPS). As a simple example of the path-integral representation we show that the state of a dynamically evolving quantum field admits a natural representation as a cMPS. A completeness argument is also provided that shows that all states in Fock space admit a cMPS representation when the number of variational parameters tends to infinity. Beyond this, we obtain a well-behaved field limit of projected entangled-pair states (PEPS) in two dimensions that provide an abstract class of quantum field states with natural symmetries. We demonstrate how symmetries of the physical field state are encoded within the dynamics of an auxiliary field system of one dimension less. In particular, the imposition of Euclidean symmetries on the physical system requires that the auxiliary system involved in the class' definition must be Lorentz-invariant. The physical field states automatically inherit entropy area laws from the PEPS class, and are fully described by the dissipative dynamics of a lower dimensional virtual field system. Our results lie at the intersection many-body physics, quantum field theory and quantum information theory, and facilitate future exchanges of ideas and insights between these disciplines.

Production and body composition traits of broilers in relation to breast weight evaluated by path analysis

Breast weight has great economic importance in poultry industry, and may be associated with other variables. This work aimed to estimate phenotypic correlations between performance (live body weight at 7 and 28 days, and at slaughter, and depth of the breast muscle measured by ultrasonography), carcass (eviscerated body weight and leg weight) and body composition (heart, liver and abdominal fat weight) traits in a broiler line, and quantify the direct and indirect influence of these traits on breast weight. Path analysis was used by expanding the matrix of partial correlation in coefficients which give the direct influence of one trait on another, regardless the effect of the other traits. The simultaneous maintenance of live body weight at slaughter and eviscerated body weight in the matrix of correlations might be harmful for statistical analysis involving systems of normal equations, like path analysis, due to the observed multicollinearity. The live body weight at slaughter and the depth of the breast muscle as measured by ultrasonography directly affected breast weight and were identified as the most responsible factors for the magnitude of the correlation coefficients obtained between the studied traits and breast weight. Individual pre-selection for these traits could favor an increased breast weight in the future reproducer candidates of this line if the broilers' environmental conditions and housing are maintained, since the live body weight at slaughter and the depth of breast muscle measured by ultrasonography were directly related to breast weight.

Azimuthal Anisotropy of pi(0) Production in Au plus Au Collisions at root s(NN)=200 GeV: Path-Length Dependence of Jet Quenching and the Role of Initial Geometry

We have measured the azimuthal anisotropy of pi(0) production for 1 < p(T) < 18 GeV/c for Au + Au collisions at root s(NN) = 200 GeV. The observed anisotropy shows a gradual decrease for 3 less than or similar to p(T) less than or similar to 7-10 GeV/c, but remains positive beyond 10 GeV/c. The magnitude of this anisotropy is underpredicted, up to at least similar to 10 GeV/c, by current perturbative QCD (PQCD) energy-loss model calculations. An estimate of the increase in anisotropy expected from initial-geometry modification due to gluon saturation effects and fluctuations is insufficient to account for this discrepancy. Calculations that implement a path-length dependence steeper than what is implied by current PQCD energy-loss models show reasonable agreement with the data.

Effective actions at finite temperature

This is a more detailed version of our recent paper where we proposed, from first principles, a direct method for evaluating the exact fermion propagator in the presence of a general background field at finite temperature. This can, in turn, be used to determine the finite temperature effective action for the system. As applications, we discuss the complete one loop finite temperature effective actions for 0+1 dimensional QED as well as for the Schwinger model in detail. These effective actions, which are derived in the real time (closed time path) formalism, generate systematically all the Feynman amplitudes calculated in thermal perturbation theory and also show that the retarded (advanced) amplitudes vanish in these theories. Various other aspects of the problem are also discussed in detail.

Superconducting current path and flux line shape in NbTiTa obtained by inter-diffusion process

This investigation presents a comprehensive characterization of magnetic and transport properties of an interesting superconducting wire, Nb-Ti -Ta, obtained through the solid-state diffusion between Nb-12 at.% Ta alloy and pure Ti. The physical properties obtained from magnetic and transport measurements related to the microstructure unambiguously confirmed a previous proposition that the superconducting currents flow in the center of the diffusion layer, which has a steep composition variation. The determination of the critical field also confirmed that the flux line core size is not constant, and in addition it was possible to determine that, in the center of the layer, the flux line core is smaller than at the borders. A possible core shape design is proposed. Among the wires studied, the one that presented the best critical current density was achieved for a diffusion layer with a composition of about Nb-32% Ti-10% Ta, obtained with a heat treatment at 700 degrees C during 120 h, in agreement with previous studies. It was determined that this wire has the higher upper critical field, indicating that the optimization of the superconducting behavior is related to an intrinsic property of the ternary alloy.

Simulated annealing with adaptive neighborhood: A case study in off-line robot path planning

Simulated annealing (SA) is an optimization technique that can process cost functions with degrees of nonlinearities, discontinuities and stochasticity. It can process arbitrary boundary conditions and constraints imposed on these cost functions. The SA technique is applied to the problem of robot path planning. Three situations are considered here: the path is represented as a polyline; as a Bezier curve; and as a spline interpolated curve. In the proposed SA algorithm, the sensitivity of each continuous parameter is evaluated at each iteration increasing the number of accepted solutions. The sensitivity of each parameter is associated to its probability distribution in the definition of the next candidate. (C) 2010 Elsevier Ltd. All rights reserved.

Does using stepwise variable selection to build sequential path analysis models make sense?

Causal inference methods - mainly path analysis and structural equation modeling - offer plant physiologists information about cause-and-effect relationships among plant traits. Recently, an unusual approach to causal inference through stepwise variable selection has been proposed and used in various works on plant physiology. The approach should not be considered correct from a biological point of view. Here, it is explained why stepwise variable selection should not be used for causal inference, and shown what strange conclusions can be drawn based upon the former analysis when one aims to interpret cause-and-effect relationships among plant traits.

Calculation of line integrals in boundary integral methods

We propose quadrature rules for the approximation of line integrals possessing logarithmic singularities and show their convergence. In some instances a superconvergence rate is demonstrated.

Bounds on integrals of the Wigner function

The integral of the Wigner function over a subregion of the phase space of a quantum system may be less than zero or greater than one. It is shown that for systems with 1 degree of freedom, the problem of determining the best possible upper and lower bounds on such an integral, over an possible states, reduces to the problem of finding the greatest and least eigenvalues of a Hermitian operator corresponding to the subregion. The problem is solved exactly in the case of an arbitrary elliptical region. These bounds provide checks on experimentally measured quasiprobability distributions.