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.

Two-Point Function at Two Loops via Triangle Diagram Insertion

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A real-time thermal field theoretical analysis of Kubo-type shear viscosity: Numerical understanding with simple examples

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

Massless and massive one-loop three-point functions in negative dimensional approach

In this article we present the complete massless and massive one-loop triangle diagram results using the negative dimensional integration method (NDIM). We consider the following cases: massless internal fields; one massive, two massive with the same mass m and three equal masses for the virtual particles. Our results are given in terms of hypergeometric and hypergeometric-type functions of the external momenta (and masses for the massive cases) where the propagators in the Feynman integrals are raised to arbitrary exponents and the dimension of the space-time is D. Our approach reproduces the known results; it produces other solutions as yet unknown in the literature as well. These new solutions occur naturally in the context of NDIM revealing a promising technique to solve Feynman integrals in quantum field theories.

Causal propagators for algebraic gauges

Applying the principle of analytic extension for generalized functions we derive causal propagators for algebraic non-covariant gauges. The so-generated manifestly causal gluon propagator in the light-cone gauge is used to evaluate two one-loop Feynman integrals which appear in the computation of the three-gluon vertex correction. The result is in agreement with that obtained through the usual prescriptions.

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.

Radiative corrections for the gauged Thirring model in causal perturbation theory

We evaluate the one-loop fermion self-energy for the gauged Thirring model in (2+1) dimensions. with one massive fermion flavor. We do this in the framework of the causal perturbation theory. In contrast to QED3, the corresponding two-point function turns out to be infrared finite on the mass shell. Then, by means of a Ward identity, we derive the on-shell vertex correction and discuss the role played by causality for non-renormalizable theories.

Correspondence between the one-loop three-point vertex and the Y and Delta electric resistor networks

Different mathematical methods have been applied to obtain the analytic result for the massless triangle Feynman diagram yielding a sum of four linearly independent (LI) hypergeometric functions of two variables F-4. This result is not physically acceptable when it is embedded in higher loops, because all four hypergeometric functions in the triangle result have the same region of convergence and further integration means going outside those regions of convergence. We could go outside those regions by using the well-known analytic continuation formulas obeyed by the F-4, but there are at least two ways we can do this. Which is the correct one? Whichever continuation one uses, it reduces a number of F-4 from four to three. This reduction in the number of hypergeometric functions can be understood by taking into account the fundamental physical constraint imposed by the conservation of momenta flowing along the three legs of the diagram. With this, the number of overall LI functions that enter the most general solution must reduce accordingly. It remains to determine which set of three LI solutions needs to be taken. To determine the exact structure and content of the analytic solution for the three-point function that can be embedded in higher loops, we use the analogy that exists between Feynman diagrams and electric circuit networks, in which the electric current flowing in the network plays the role of the momentum flowing in the lines of a Feynman diagram. This analogy is employed to define exactly which three out of the four hypergeometric functions are relevant to the analytic solution for the Feynman diagram. The analogy is built based on the equivalence between electric resistance circuit networks of types Y and Delta in which flows a conserved current. The equivalence is established via the theorem of minimum energy dissipation within circuits having these structures.

The Epstein-Glaser causal approach to the light-front QED(4). II: Vacuum polarization tensor

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

Eletrodinâmica quântica generalizada a la teoria de perturbação causal

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Susceptibility of citrus species to Alternaria alternata, the causal agent of the Alternaria brown spot

Alternaria alternata, the causal agent of Alternaria brown spot (ABS), causes necrosis on leaves, twigs, and fruit, reducing the productivity and quality of fruits. Tangerines and their hybrids are highly susceptible to the disease. Species, hybrids, and cultivars of Citrus from the germplasm bank of the Estacao Experimental de Citricultura de Bebedouro, São Paulo, Brazil, were evaluated in 2004 and 2005 with respect to their resistance to A. alternata, both through natural infection and by inoculation. Detached leaves were also used to demonstrate susceptibility or resistance to the disease. Ten cultivars of Satsumas (Citrus unshiu), and 14 cultivars of Clementine mandarin (C. clementina) did not show any symptoms of the disease in their leaves, either through natural infection or when inoculated in the field. The Burguess SRA-412, Wallent SRA-438, Carvalhais, Ampefy SRA-459, Ananas SRA, and Macaque SRA-426 mandarin hybrids (C. reticulata) did not show symptoms of the disease under natural or artificial infection in the field. Some cultivars of C. deliciosa, C. tangerina, C. erythrosa, and C. temple showed symptoms of the disease, even though no previous record of their susceptibility to Alternaria brown spot had been previously reported. The hybrids Fairchild, Nova, Page, Fortune, and Sunburst were susceptible to the disease. However, Fremont mandarin (a crossing between C. clementina and C. reticulata), Encore (C. nobilis x C. deliciosa), and Fallglo (C. reticulata x C. paradisi) did not show symptoms in field, and few symptoms were verified in detached leaves. These materials are promising for the cultivation of tangerines, and will enable genetic improvement for the development of cultivars resistant to Alternaria brown spot. (c) 2007 Elsevier B.V. All rights reserved.

Biofertilizer for control of Guignardia citricarpa, the causal agent of citrus black spot

Biofertilizers generated from the anaerobic and aerobic digestion of cattle manure, known as Bio1 and Bio2, respectively, were studied with regard to their microbial composition and effect on the mycelial growth of Phyllosticta citricarpa, the causal agent of citrus black spot (CBS). Two field experiments were conducted to determine the biofertilizer's potential (Bio1) in controlling CBS (2001/2002 and 2002/2003 crops). It was observed that the greatest number of microorganisms was found in the aerobically produced biofertilizer. Bio2 did not inhibit the mycelial growth of P. citricarpa. Mycelial growth of P. citricarpa was inversely proportional to the Bio1 biofertilizer concentration. In the 2001/2002 cropping season, the Biol effect in controlling CBS was directly proportional to its concentration, at the rate of 0 (healthy fruit), with R-2 = 0.88. Biol had a significant effect in controlling CBS, at a concentration of 10%, during the 2001/2002 cropping season, with DI values of 0.246 and 0.229 for the. 10 and 20% doses, respectively, compared to DI of 0.329 for the control. A directly proportional effect of the biofertilizer concentration on the percentage of fruits with a rating of zero was. also observed in the 2002/2003 cropping season, with R-2 = 0.48. However, even at doses higher than in the preceding cropping season, the biofertilizer was less effective, possibly due to a higher occurrence of the disease. Copper oxychloride and combined applications of copper oxychloride and carbendazim plus mancozeb controlled the disease. The possibility of using the biofertilizer as a protective biofungicide to replace copper oxychloride, especially in organic agriculture, should be explored. (c) 2005 Elsevier Ltd. All rights reserved.

Controle alternativo de Colletotrichum acutatum agente causal da queda prematura dos frutos cítricos

A queda prematura dos frutos cítricos (QPFC), causada por Colletotrichum acutatum, dados os grandes prejuízos que têm causado aos produtores, constitui-se numa doença de grande importância econômica. O controle da doença é feito predominantemente mediante uso de fungicidas, que eleva o custo de produção e afeta negativamente o meio ambiente. Diante disso, este trabalho teve por objetivo buscar um método alternativo de controle da QPFC, mediante o uso de agentes de biocontrole ou de biofertilizantes. Diferentes concentrações de biofertilizantes (originários de duas fontes distintas e denominados de Bio1 e Bio 2); três isolados de Bacillus subtilis (ACB-69; 72 e 77) e três isolados de Trichoderma spp. (ACB-14; 37 e 39) foram testados, isoladamente ou em combinação, sob condições de laboratório, quanto à capacidade inibitória da germinação de conídios de C. acutatum. Estudaram-se, ainda, a produção de metabólitos termoestáveis por B. subtilis e o efeito sobre a germinação do patógeno. Quinze isolados de B. subtilis foram testados quanto à capacidade de prevenir a infecção por C. acutatum em flores destacadas de lima- ácida 'Tahiti' e, no campo, foram instalados dois experimentos, visando a testar ACBs e biofertilizantes no controle da doença. Verificou-se que o isolado ACB-72 (B. subtilis) e ACB-37 (T. pseudokoningii) foram os que mais inibiram a germinação do patógeno. Quanto à produção de metabólitos termoestáveis, ACB-69 e 77 foram os mais eficientes em produzir substâncias antifúngicas, e em quantidades suficientes para inibirem a germinação do patógeno. A mistura dos quatro isolados de Bacillus (ACBs: 69; 72; 77 e AP3) foi o que apresentou maior porcentagem de inibição (73%). Os biofertilizantes (Bio1 e Bio2), em concentrações acima de 10% e, quando em associação com isolados de Trichoderma spp., promoveram maiores inibições na germinação de C. acutatum. em testes com flores destacadas, verificou-se que, onde foram aplicados os ACBs 69; 76; 74 e 77, as porcentagens de pétalas sem sintomas de infecção por C. acutatum foram de 83; 92; 92 e 97%, respectivamente. Mediante avaliações a campo, verificou-se a potencialidade de B. subtilis e de biofertilizantes em controlar a doença.

Controle biológico de Colletotrichum acutatum, agente causal da queda prematura dos frutos cítricos

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

Influência da temperatura e da luminosidade no desenvolvimento de Guignardia citricarpa, agente causal da mancha preta dos frutos cítricos

O presente trabalho teve como objetivo avaliar sob condições de laboratório, o efeito de temperatura (15, 18, 20, 21, 24, 25, 27, 30, 33 e 35 ± 1 ºC) nas condições escuro, luz contínua e fotoperíodo 12/12 h, na produção de pseudotécios de isolados de Guignardia citricarpa, provenientes de regiões cítricolas dos Estados de São Paulo e Rio de Janeiro. Discos de folhas de limoeiro 'Cravo' (Citrus limonia), de 12 mm de diâmetro, foram autoclavados e depositadas (parte abaxial) na superfície do meio de cultura constituído por ágar-água 2%. Foram colocados quatro discos de folhas por placa onde, de forma conjunta e intercalar aos mesmos, depositaram-se dois discos obtidos de colônias de Phyllosticta citricarpa, com 21 dias de incubação. Foi, também, estudado o efeito da temperatura e do tempo de incubação (2, 8 e 16 h) na germinação dos ascósporos. Após 21 dias de incubação, a ótima temperatura ajustada pela função beta generalizada, para produção de pseudotécios deu-se a 26 e 22,5 a 27,5 °C, sob condição de escuro e de luz, respectivamente. Observou-se também produção de pseudotécios a 27 ºC em fotoperíodo 12/12 h. em estudo complementar foi verificado que, aos 19 dias, a 27 ºC, cerca de 90% dos pseudotécios haviam alcançado a maturidade, com abundante produção de ascósporos. A maior porcentagem de ascósporos germinados foi constatada na temperatura de 24 ºC, após 16 h de incubação. Dentre as vantagens alcançadas, incluem-se a possibilidade (i) da produção massal de ascósporos em curto período de tempo, e (ii) da padronização do inóculo, tanto qualitativa, quanto quantitativa.