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.

Negative dimensional approach for scalar two-loop three-point and three-loop two-point integrals

The well-known D-dimensional Feynman integrals were shown, by Halliday and Ricotta, to be capable of undergoing analytic continuation into the domain of negative values for the dimension of space-time. Furthermore, this could be identified with Grassmannian integration in positive dimensions. From this possibility follows the concept of negative-dimensional integration for loop integrals in field theories. Using this technique, we evaluate three two-loop three-point scalar integrals, with five and six massless propagators, with specific external kinematic configurations (two legs on-shell), and four three-loop two-point scalar integrals. These results are given for arbitrary exponents of propagators and dimension, in Euclidean space, and the particular cases compared to results published in the literature.

Non-planar double-box, massive and massless pentabox Feynman integrals in the negative-dimensional approach

The negative-dimensional integration method is a technique which can be applied, with success, in usual covariant gauge calculations. We consider three two-loop diagrams: the scalar massless non-planar double-box with six propagators and the scalar pentabox in two cases, where six virtual particles have the same mass, and in the case all of them are massless. Our results are given in terms of hypergeometric functions of Mandelstam variables and also for arbitrary exponents of propagators and dimension D.

NDIM achievements: massive, arbitrary tensor rank and N-loop insertions in Feynman integrals

One of the main difficulties in studying quantum field theory, in the perturbative regime, is the calculation of D-dimensional Feynman integrals. In general, one introduces the so-called Feynman parameters and, associated with them, the cumbersome parametric integrals. Solving these integrals beyond the one-loop level can be a difficult task. The negative-dimensional integration method (NDIM) is a technique whereby such a problem is dramatically reduced. We present the calculation of two-loop integrals in three different cases: scalar ones with three different masses, massless with arbitrary tensor rank, with and N insertions of a two-loop diagram.

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.

One-loop superstring amplitude from integrals on pure spinors space

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

The cohomology of superspace, pure spinors and invariant integrals

The superform construction of supersymmetric invariants, which consists of integrating the top component of a closed superform over spacetime, is reviewed. The cohomological methods necessary for the analysis of closed superforms are discussed and some further theoretical developments presented. The method is applied to higher-order corrections in heterotic string theory up to alpha'(3). Some partial results on N = 2, d = 10 and N = 1, d = 11 are also given.

Effects of oscillatory behavior of the dipole function on the dissociation dynamics of the classical driven Morse oscillator

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

Semilinear parabolic problems in thin domains with a highly oscillatory boundary

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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).

CIRCADIAN OSCILLATORY PATTERNS OF OXYGEN-UPTAKE IN INDIVIDUAL WORKERS OF THE ANT CAMPONOTUS-RUFIPES

Respiratory rates of individual workers of Camponotus rufipes Fabricius (Hymenoptera: Formicidae) were measured at 25-degrees-C and LD 12:12 h (lights on 06.00 hours), DL 12:12 h (lights on 18.00 hours), LL (850 lux) and DD (red light, 20-30 lux), using the micro-Warburg technique. Worker ants were collected from natural nest during the winter of 1987 in a woodland park in the region of Rio Claro, São Paulo, Brazil. The respiration of ants showed a circadian rhythm with acrophase ranging from 20 h 41 min to 01 h 18 min and from 10 h 32 min to 12 h 22 min at LD and DD, respectively. In constant darkness the rhythmometric variables were similar to those presented by ants kept at LD 12:12 h. Under constant light no circadian rhythm in the respiration rates was found. A reduction in the amplitude was observed, indicating an inhibitory effect of this light regime on the respiration process.

In vitro evaluation of root canal preparation using oscillatory and rotary systems in flattened root canals

Objective: the aim of this study was to evaluate the biomechanical preparation of flattened root canals using the following systems: Endo-Eze AET stainless steel oscillatory instruments (Ultradent) and RaCe rotary NiTi instruments (FKG Dentaire). Materials and Methods: Twenty extracted human mandibular incisors were randomly assigned to two groups: Group I Instrumentation with oscillatory Endo-Eze AET files (oscillatory technique); Group 2 - Instrumentation with rotary NiTi RaCe files (rotary technique). The teeth were decoronated, had their apices and coronal openings sealed with sticky wax and were embedded in crystal-clear orthophtalic polyester resin. The roots were sectioned transversally with diamond discs at 10 mm (middle third) and 5 mm (apical third) from the apex and the segments were reassembled for instrumentation. The sections were photographed before and after root canal instrumentation and evaluated with respect to whether the original root canal shape was modified by instrumentation. To evaluate the differences in the root canal shape before and after biomechanical preparation, scores were given regarding the instruments touch on the intracanal walls. Results: In middle third of the root canals instrumented with the rotary system, there was a change in the original canal anatomy (p < 0.05), with formation of a protuberance in the mesiodistal direction. This protuberance did not occur when the oscillatory instrumentation was used. The oscillatory system had better results in the middle and apical thirds as evaluated by Dunn's multiple-comparison test (p > 0.05). Conclusion: Under the tested conditions, Endo-Eze oscillatory system yielded the instrumentation of all flattened oot canal walls, maintaining the canal original shape throughout the biomechanical preparation, and was more effective than RaCe rotary system.

Carbon monoxide oxidation over platinum: Stable, oscillatory and quasi-chaotic regimes

We model the heterogeneously catalyzed oxidation of CO over a Pt surface. A phase diagram analysis is used to probe the several steady state regimes and their stability. We incorporate an experimentally observed 'slow' sub-oxide kinetic step, thereby generalizing a previously presented model. In agreement with experimental data, stable, oscillatory and quasi-chaotic regimes are obtained. Furthermore, the inclusion of the sub-oxide step yields a relaxation oscillation regime. © 1998 Elsevier Science B.V. All rights reserved.

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.