EIGENVALUES of FIBONACCI STOCHASTIC ADDING MACHINE

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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.

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)

Stochastic variational approach applied to 2, 3 and 4 alpha particles

A stochastic variational method is applied to calculate the binding energies and root-mean-square radii of 2, 3 and 4 alpha particles using an S-wave Ali-Bodmer potential. The results agree with other calculations. We discuss the application of the present method to study the universality in weakly-bound three and four-body systems in the context of ultracold atomic traps.

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.

Stochastic Skellam model

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Crossover between the extended and localized regimes in stochastic partially self-avoiding walks in one-dimensional disordered systems

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Stochastic quantization of real-time thermal field theory

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Correlation times in stochastic equations with delayed feedback and multiplicative noise

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)