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.

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.

Reply to Comment on 'validity of Feynman's prescription of disregarding the Pauli principle in intermediate states'

In a recent paper, we raised a question on the validity of Feynman's prescription of disregarding the Pauli principle in intermediate states of perturbation theory. In the preceding Comment, Cavalcanti correctly pointed out that Feynman's prescription is consistent with the exact solution of the model that we used. This means that the Pauli principle does not necessarily apply to intermediate states. We discuss implications of this puzzling aspect.

Validity of Feynman's prescription of disregarding the Pauli principle in intermediate states

Regarding the Pauli principle in quantum field theory and in many-body quantum mechanics, Feynman advocated that Pauli's exclusion principle can be completely ignored in intermediate states of perturbation theory. He observed that all virtual processes (of the same order) that violate the Pauli principle cancel out. Feynman accordingly introduced a prescription, which is to disregard the Pauli principle in all intermediate processes. This ingenious trick is of crucial importance in the Feynman diagram technique. We show, however, an example in which Feynman's prescription fails. This casts doubts on the general validity of Feynman's prescription. [S1050-2947(99)04604-1].

Feynman & Gell-Mann: Luzes, Quarks, Ação!

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Systematic consideration of petiole anatomy of species of Echinodorus Richard (Alismataceae) from north-eastern Brazil

Petiole anatomy of the north-eastern Brazilian species Echinodorus glandulosus, E. palaefolius, E. pubescens, E subalatus, E lanceolatus and E paniculatus were examined. All species had petioles with an epidermis composed of tabular cells with thin walls. The chlorenchyma just below the epidermis alternates with collateral vascular bundles. The interior of the petiole is filled by aerenchyma with ample open spaces or lacunas. The lacunas are bridged at intervals by plates, or by diaphragm-like linkages. There are lactiferous ducts and groups of fibres throughout the entire length of the petiole, but more frequently in the chlorenchyma. Important taxonomic characteristics for the genus Echinodorus include the shape and outline of the petiole in transversal section, the presence of winged extensions, and the number of vascular bundle arcs. Exceptions occur in E. lanceolatus and E. paniculatus, whose petioles have similar anatomic patterns. A comparative chart of the petiole anatomic characteristics analyzed is presented. (c) 2007 Elsevier GmbH. All rights reserved.

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.

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.

Cálculos de integrais de Feynman em teorias de campos

Pós-graduação em Física - IFT

Estudo analítico de alguns aspectos da dinâmica na frente de luz: transformações de Lorentz, sistemas de dois corpos em interação, polarização do vácuo e integrais de Feynman

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Suicídio, da identificação com a mãe morta ao resgate narcísico: um estudo psicanalítico do personagem Richard Brown do filme As horas

O tema desta Dissertação é o suicídio como conseqüência da identificação com a mãe morta. Trata-se de uma pesquisa teórica fundamentada na teoria psicanalítica, que recorre à análise do personagem Richard Brown, do filme As Horas, para ilustrar o argumento teórico de que a revivescência da identificação com a mãe morta pode ser um fator desencadeante do suicídio do melancólico na vida adulta. Inicialmente procura explicitar o conceito de mãe morta, caracterizada como uma mãe que mesmo quando está presente mostra-se ausente nos cuidados e no investimento amoroso ao filho em função de sua depressão. Assim, para a criança, a imagem materna será a de uma mãe sem vida, de uma mãe morta. Mostra a identificação com a mãe morta como saída psíquica para a situação traumática proveniente do desinvestimento amoroso maternal. A criança na relação com esta mãe vive uma catástrofe psíquica chamada por Green de trauma narcisista, o que vai determinar o destino do investimento libidinal, objetal e narcisista do sujeito. Assim sendo, considera-se a melancolia como uma psicopatologia manifestada na vida adulta pelo sujeito subjugado pelo complexo da mãe morta. O estudo da melancolia no texto Luto e Melancolia, de Freud, fornece subsídios para se compreender os processos do mundo interior daqueles que querem dar cabo à sua própria existência. A melancolia evidencia o embate entre o Eu e o Supereu nos papéis de acusado e acusador. Mostra que o Supereu se torna sádico ao cobrar perfeição do Eu masoquista empobrecido narcisicamente pela identificação com a mãe morta. Quando chega às raias do sadismo esse embate leva o Eu, identificado com a mãe morta, a desejar eliminar o objeto mau introjetado numa parte do Eu, para resgatar o seu valor narcísico idealizado. Aponta o suicídio como a saída psíquica encontrada pelo melancólico para livrar-se da identificação com a mãe morta. Conclui que no suicídio os conflitos inconscientes manifestados na vida adulta são revivescências dos conteúdos psíquicos registrados na infância. No caso estudado em questão, a revivescência da identificação com a mãe morta teria sido o fator desencadeante do suicídio de Richard Brown na vida adulta.