EVALUATING ONE-LOOP LIGHT-CONE INTEGRALS BY COVARIANTIZING THE GAUGE-DEPENDENT POLE

Making sure that causality be preserved by means of ''covariantizing'' the gauge-dependent singularity in the propagator of the vector potential A(mu)(x), we show that the evaluation of some basic one-loop light-cone integrals reproduce those results obtained through the Mandelstam-Leibbrandt prescription. Moreover, such a covariantization has the advantage of leading to simpler integrals to be performed in the cone variables (the bonus), although, of course, it introduces an additional alpha-parameter integral to be performed (the price to pay).

Third body perturbation using a single averaged model considering elliptic orbits for the disturbing body

In the present work, we expanded the study done by Solorzanol(1) including the eccentricity of the perturbing body. The assumptions used to develop the single-averaged analytical model are the same ones of the restricted elliptic three-body problem. The disturbing function was expanded in Legendre polynomials up to fourth-order. After that, the equations of motion are obtained from the planetary equations and we performed a set of numerical simulations. Different initial eccentricities for the perturbing and perturbed body are considered. The results obtained perform an analysis of the stability of a near-circular orbits and investigate under which conditions this orbit remain near-circular.

Probing negative-dimensional integration: Two-loop covariant vertex and one-loop light-cone integrals

The negative-dimensional integration method (NDIM) seems to be a very promising technique for evaluating massless and/or massive Feynman diagrams. It is unique in the sense that the method gives solutions in different regions of external momenta simultaneously. Moreover, it is a technique whereby the difficulties associated with performing parametric integrals in the standard approach are transferred to a simpler solving of a system of linear algebraic equations, thanks to the polynomial character of the relevant integrands. We employ this method to evaluate a scalar integral for a massless two-loop three-point vertex with all the external legs off-shell, and consider several special cases for it, yielding results, even for distinct simpler diagrams. We also consider the possibility of NDIM in non-covariant gauges such as the light-cone gauge and do some illustrative calculations, showing that for one-degree violation of covariance (i.e. one external, gauge-breaking, light-like vector n μ) the ensuing results are concordant with the ones obtained via either the usual dimensional regularization technique, or the use of the principal value prescription for the gauge-dependent pole, while for two-degree violation of covariance - i.e. two external, light-like vectors n μ, the gauge-breaking one, and (its dual) n * μ - the ensuing results are concordant with the ones obtained via causal constraints or the use of the so-called generalized Mandelstam-Leibbrandt prescription. © 1999 Elsevier Science B.V.

Feynman integrals with tensorial structure in the negative dimensional integration scheme

The negative-dimensional integration method (NDIM) is revealing itself as a very useful technique for computing massless and/or massive Feynman integrals, covariant and noncovanant alike. Up until now however, the illustrative calculations done using such method have been mostly covariant scalar integrals/without numerator factors. We show here how those integrals with tensorial structures also can be handled straightforwardly and easily. However, contrary to the absence of significant features in the usual approach, here the NDIM also allows us to come across surprising unsuspected bonuses. Toward this end, we present two alternative ways of working out the integrals and illustrate them by taking the easiest Feynman integrals in this category that emerge in the computation of a standard one-loop self-energy diagram. One of the novel and heretofore unsuspected bonuses is that there are degeneracies in the way one can express the final result for the referred Feynman integral.

Some integrals occurring in a topology change problem

In a paper presented a few years ago, de Lorenci et al. showed, in the context of canonical quantum cosmology, a model which allowed space topology changes. The purpose of this present work is to go a step further in that model, by performing some calculations only estimated there for several compact manifolds of constant negative curvature, such as the Weeks and Thurston spaces and the icosahedral hyperbolic space (Best space). ©2000 The American Physical Society.

Prescriptionless light-cone integrals

Perturbative quantum gauge field theory as seen within the perspective of physical gauge choices such as the light-cone gauge entails the emergence of troublesome poles of the type (k · n)-α in the Feynman integrals. These come from the boson field propagator, where α = 1, 2, ⋯ and nμ is the external arbitrary four-vector that defines the gauge proper. This becomes an additional hurdle in the computation of Feynman diagrams, since any graph containing internal boson lines will inevitably produce integrands with denominators bearing the characteristic gauge-fixing factor. How one deals with them has been the subject of research over decades, and several prescriptions have been suggested and tried in the course of time, with failures and successes. However, a more recent development at this fronteer which applies the negative dimensional technique to compute light-cone Feynman integrals shows that we can altogether dispense with prescriptions to perform the calculations. An additional bonus comes to us attached to this new technique, in that not only it renders the light-cone prescriptionless but, by the very nature of it, it can also dispense with decomposition formulas or partial fractioning tricks used in the standard approach to separate pole products of the type (k · n)-α[(k - p) · n]-β (β = 1, 2, ⋯). In this work we demonstrate how all this can be done.

Loop Integrals in Three Outstanding Gauges: Feynman, Light-Cone, and Coulomb

We apply the negative dimensional integration method (NDIM) to three outstanding gauges: Feynman, light-cone, and Coulomb gauges. Our aim is to show that NDIM is a very suitable technique to deal with loop integrals, regardless of which gauge choice that originated them. In the Feynman gauge we perform scalar two-loop four-point massless integrals; in the light-cone gauge we calculate scalar two-loop integrals contributing to two-point functions without any kind of prescriptions, since NDIM can abandon such devices - this calculation is the first test of our prescriptionless method beyond one-loop order; and finally, for the Coulomb gauge we consider a four-propagator massless loop integral, in the split-dimensional regularization context. © 2001 Academic Press.

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.

Stresses analysis in semi-elliptic leaf spring and comparison with the SAE J788 (1982) norm

In this work are presented the values found with the experimental testing, in the semi-elliptic leaf spring, utilizing 24 strain gages, distributed in five leaves of springs; these values have been compared to the calculated values found with the application of Norm SAE J788 (1982). The results showed discrepancy between the values measured and calculated and that the Norm is not indicated to determine the actuating stress in any point of any leaf of the leaf spring, but due to its simplicity and quickness of the process it presents good precision for the pre-development of the product. Copyright © 2002 Society of Automotive Engineers, Inc.

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.

Third-body perturbation in the case of elliptic orbits for the disturbing body

In the present work it is presented a semi-analytical and a numerical study of the perturbation caused in a spacecraft by a third body using a double averaged analytical model with the disturbing function expanded in Legendre polynomials up to the second-order. The important reason for this procedure is to eliminate the terms due to the short time periodic motion of the spacecraft and to show smooth curves for the evolution of the mean orbital elements for a long time period. The aim of this study is to calculate the effect of lunar perturbations on the orbits of spacecrafts that are traveling around the Earth. It is presented an analysis of the stability of a near-circular orbit and a study to know under which conditions this orbit remains near-circular. A study of the equatorial orbits is also performed.

Measurement of the elliptic anisotropy of charged particles produced in PbPb collisions at √sNN=2.76 TeV

The anisotropy of the azimuthal distributions of charged particles produced in √sNN=2.76 TeV PbPb collisions is studied with the CMS experiment at the LHC. The elliptic anisotropy parameter, v2, defined as the second coefficient in a Fourier expansion of the particle invariant yields, is extracted using the event-plane method, two- and four-particle cumulants, and Lee-Yang zeros. The anisotropy is presented as a function of transverse momentum (pT), pseudorapidity (η) over a broad kinematic range, 0.3elliptic anisotropy is found to obey a universal scaling with the transverse particle density for different collision systems and center-of-mass energies. © 2013 CERN. Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Periodic solutions for nonlinear telegraph equationvia elliptic regularization

ABSTRACT: In this work we are concerned with the existence and uniqueness of T -periodic weak solutions for an initial-boundary value problem associated with nonlinear telegraph equations typein a domain. Our arguments rely on elliptic regularization technics, tools from classical functional analysis as well as basic results from theory of monotone operators.

Existence of solutions for a class of degenerate quasilinear elliptic equation in R-N with vanishing potentials

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)