Path integrals on a flux cone

This paper considers the Schrodinger propagator on a cone with the conical singularity carrying magnetic flux (flux cone). Starting from the operator formalism, and then combining techniques of path integration in polar coordinates and in spaces with constraints, the propagator and its path integral representation are derived. The approach shows that effective Lagrangian contains a quantum correction term and that configuration space presents features of nontrivial connectivity.

A RIEMANN INTEGRAL APPROACH TO FEYNMANS PATH-INTEGRAL

It is a well known result that the Feynman's path integral (FPI) approach to quantum mechanics is equivalent to Schrodinger's equation when we use as integration measure the Wiener-Lebesgue measure. This results in little practical applicability due to the great algebraic complexibity involved, and the fact is that almost all applications of (FPI) - ''practical calculations'' - are done using a Riemann measure. In this paper we present an expansion to all orders in time of FPI in a quest for a representation of the latter solely in terms of differentiable trajetories and Riemann measure. We show that this expansion agrees with a similar expansion obtained from Schrodinger's equation only up to first order in a Riemann integral context, although by chance both expansions referred to above agree for the free. particle and harmonic oscillator cases. Our results permit, from the mathematical point of view, to estimate the many errors done in ''practical'' calculations of the FPI appearing in the literature and, from the physical point of view, our results supports the stochastic approach to the problem.

Quantum propagator for some classes of three-dimensional three-body systems

In this work we solve exactly a class of three-body propagators for the most general quadratic interactions in the coordinates, for arbitrary masses and couplings. This is done both for the constant as the time-dependent couplings and masses, by using the Feynman path integral formalism. Finally, the energy spectrum and the eigenfunctions are recovered from the propagators. © 2005 Elsevier Inc. All rights reserved.

EFFICIENT FAULT LOCATION IN UNDERGROUND DISTRIBUTION SYSTEMS THROUGH OPTIMUM-PATH FOREST

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

An Optimum-Path Forest framework for intrusion detection in computer networks

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Efficient supervised optimum-path forest classification for large datasets

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A New Approach for Nontechnical Losses Detection Based on Optimum-Path Forest

Nowadays, fraud detection is important to avoid nontechnical energy losses. Various electric companies around the world have been faced with such losses, mainly from industrial and commercial consumers. This problem has traditionally been dealt with using artificial intelligence techniques, although their use can result in difficulties such as a high computational burden in the training phase and problems with parameter optimization. A recently-developed pattern recognition technique called optimum-path forest (OPF), however, has been shown to be superior to state-of-the-art artificial intelligence techniques. In this paper, we proposed to use OPF for nontechnical losses detection, as well as to apply its learning and pruning algorithms to this purpose. Comparisons against neural networks and other techniques demonstrated the robustness of the OPF with respect to commercial losses automatic identification.

Design of a simple detection cell with extended optical path length for capillary electrophoresis: Application to multiresidue pesticide analysis

Absorbance detection in capillary electrophoresis (CE), offers an excellent mass sensitivity, but poor concentration detection limits owing to very small injection volumes (normally I to 10 nL). This aspect can be a limiting factor in the applicability of CE/UV to detect species at trace levels, particularly pesticide residues. In the present work, the optical path length of an on-column detection cell was increased through a proper connection of the column (75 mu m i.d.) to a capillary detection cell of 180 mu m optical path length in order to improve detectability. It is shown that the cell with an extended optical path length results in a significant gain in terms of signal to noise ratio. The effect of the increase in the optical path length has been evaluated for six pesticides, namely, carbendazim, thiabendazole, imazalil, procymidone triadimefon, and prochloraz. The resulting optical enhancement of the detection cell provided detection limits of ca. 0.3 mu g/mL for the studied compounds, thus enabling the residue analysis by CE/UV.

The temperature coefficient of the optical path length as a function of the temperature in different optical glasses

An interferometric technique was used to determine the temperature coefficient of the optical path length (dS/dT) as a function of the temperature in several optical glasses. The temperature range was between 25degreesC and 180degreesC. The studied samples included undoped and doped oxide glasses, such as low silica calcium aluminosilicate, phosphates, borates and also chalcogenides. The oxide glasses had dS/dT between 10 X 10(-6) K-1 and 20x10(-6) K-1, while for the chalcogenides, these were around 70 x 10(-6)K(-1). The results showed that dS/dTs increased with the temperature in all samples. For samples doped with Nd the dS/dT values were found to be independent of concentration. on the other hand, for the phosphate glass doped with Cr, dS/dT increased about 5% when compared with the Nd doped one. In conclusion, the used interferometric method, which is a considerably simpler and a lower cost technique, and is a useful tool to measure dS/dT in semi-transparent glasses as a function of the composition and temperature. (C) 2004 Elsevier B.V. All rights reserved.

Inversion in the temperature coefficient of the optical path length close to the glass transition temperature in tellurite glasses

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Asymptotics of zeros of polynomials arising from rational integrals

We prove that the zeros of the polynomials P.. (a) of degree m, defined by Boros and Moll via[GRAPHICS]approach the lemmiscate {zeta epsilon C: \zeta(2) - 1\ = Hzeta < 0}, as m --> infinity. (C) 2004 Elsevier B.V. All rights reserved.

NONDEGENERATE UMBILICS, THE PATH FORMULATION and GRADIENT BIFURCATION PROBLEMS

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Light-cone gauge integrals: prescriptionlessness at two loops

The only calculations performed beyond one-loop level in the light-cone gauge make use of the Mandelstam-Leibbrandt (ML) prescription in order to circumvent the notorious gauge dependent poles. Recently we have shown that in the context of negative dimensional integration method (NDIM) such prescription can be altogether abandoned, at least in one-loop order calculations. We extend our approach, now studying two-loop integrals pertaining to two-point functions. While previous works on the subject present only divergent parts for the integrals, we show that our prescriptionless method gives the same results for them, besides finite parts for arbitrary exponents of propagators. (C) 2000 Elsevier B.V. B.V. All rights reserved.

One-loop n-point equivalence among negative-dimensional, Mellin-Barnes and Feynman parametrization approaches to Feynman integrals

We show that at one-loop order, negative-dimensional, Mellin-Barnes (MB) and Feynman parametrization (FP) approaches to Feynman loop integral calculations are equivalent. Starting with a generating functional, for two and then for n-point scalar integrals, we show how to reobtain MB results, using negative-dimensional and FP techniques. The n-point result is valid for different masses, arbitrary exponents of propagators and dimension.

A systematization for one-loop 4D Feynman integrals

We present a strategy for the systematization of manipulations and calculations involving divergent (or not) Feynman integrals, typical of the one-loop perturbative solutions of QFT, where the use of an explicit regularization is avoided. Two types of systematization are adopted. The divergent parts are put in terms of a small number of standard objects, and a set of structure functions for the finite parts is also defined. Some important properties of the finite structures, specially useful in the verification of relations among Green's functions, are identified. We show that, in fundamental (renormalizable) theories, all the finite parts of two-, three- and four-point functions can be written in terms of only three basic functions while the divergent parts require (only) five objects. The final results obtained within the proposed strategy can be easily converted into those corresponding to any specific regularization technique providing an unified point of view for the treatment of divergent Feynman integrals. Examples of physical amplitudes evaluation and their corresponding symmetry relations verification are presented as well as generalizations of our results for the treatment of Green's functions having an arbitrary number of points are considered.