Negative-dimensional integration revisited

Feynman diagrams are the best tool we have to study perturbative quantum field theory. For this very reason the development of any new technique that allows us to compute Feynman integrals is welcome. By the middle of the 1980s, Halliday and Ricotta suggested the possibility of using negative-dimensional integrals to tackle the problem. The aim of this work is to revisit the technique as such and check on its possibilities. For this purpose, we take a box diagram integral contributing to the photon-photon scattering amplitude in quantum electrodynamics using the negative-dimensional integration method. Our approach enables us to quickly reproduce the known results as well as six other solutions as yet unknown in the literature. These six new solutions arise quite naturally in the context of negative-dimensional integration method, revealing a promising technique to handle Feynman integrals.

Semiclassical particle spectrum of double sine-Gordon model

We present new theoretical results on the spectrum of the quantum field theory of the double sine-Gordon model. This non-integrable model displays different varieties of kink excitations and bound states thereof. Their mass can be obtained by using a semiclassical expression of the matrix elements of the local fields. In certain regions of the coupling-constants space the semiclassical method provides a picture which is complementary to the one of the form factor perturbation theory, since the two techniques give information about the mass of different types of excitations. In other regions the two methods are comparable, since they describe the same kind of particles. Furthermore, the semiclassical picture is particularly suited to describe the phenomenon of false vacuum decay, and it also accounts in a natural way the presence of resonance states and the occurrence of a phase transition. (C) 2004 Elsevier B.V. All rights reserved.

The two-loop massless (lambda/4!)phi(4) model in nontranslational invariant domain

We study the (lambda/4!)phi(4) massless scalar field theory in a four-dimensional Euclidean space, where all but one of the coordinates are unbounded. We are considering Dirichlet boundary conditions in two hyperplanes, breaking the translation invariance of the system. We show how to implement the perturbative renormalization up to two-loop level of the theory. First, analyzing the full two and four-point functions at the one-loop level, we show that the bulk counterterms are sufficient to render the theory finite. Meanwhile, at the two-loop level, we must also introduce surface counterterms in the bare Lagrangian in order to make finite the full two and also four-point Schwinger functions. (c) 2006 American Institute of Physics.

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].

Lorentz Connections and Gravitation

The different roles played by Lorentz connections in general relativity and in teleparallel gravity are reviewed. Some of the consequences of this difference are discussed.

NOISE and ULTRAVIOLET DIVERGENCES IN SIMULATIONS of GINZBURG-LANDAU-LANGEVIN TYPE of EQUATIONS

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Gap solitons in a model of a superfluid fermion gas in optical lattices

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

Renormalization of singular potentials and power counting

We use a toy model to illustrate how to build effective theories for singular potentials. We consider a central attractive 1/r(2) potential perturbed by a 1/r(4) correction. The power-counting rule, an important ingredient of effective theory, is established by seeking the minimum set of short-range counterterms that renormalize the scattering amplitude. We show that leading-order counterterms are needed in all partial waves where the potential overcomes the centrifugal barrier, and that the additional counterterms at next-to-leading order are the ones expected on the basis of dimensional analysis. (C) 2008 Elsevier B.V. All rights reserved.

Langevin simulation of scalar fields: Additive and multiplicative noises and lattice renormalization

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

FROM DIRAC ACTION TO ELKO ACTION

A fundamental action, representing a mass dimension-transmuting operator between Dirac and ELKO spinor fields, is performed on the Dirac Lagrangian, in order to lead it into the ELKO Lagrangian. Such a dynamical transformation can be seen as a natural extension of the Standard Model that incorporates dark matter fields. The action of the mass dimension-transmuting operator on a Dirac spinor field, that de fines and introduces such a mapping, is shown to be a composition of the Dirac operator and the nonunitary transformation that maps Dirac spinor fields into ELKO spinor fields, de fined in J. Math. Phys. 4 8, 123517 (2007). This paper gives allowance for ELKO, as a candidate to describe dark matter, to be incorporated in the Standard Model. It is intended to present for the first time, up to our knowledge, the dynamical character of a mapping between Dirac and ELKO spinor fields, transmuting the mass dimension of spin one-half fermionic fields from 3/2 to 1 and from 1 to 3/2.

Self-dual hopfions

We construct static and time-dependent exact soliton solutions with nontrivial Hopf topological charge for a field theory in 3 + 1 dimensions with the target space being the two dimensional sphere S(2). The model considered is a reduction of the so-called extended Skyrme-Faddeev theory by the removal of the quadratic term in derivatives of the fields. The solutions are constructed using an ansatz based on the conformal and target space symmetries. The solutions are said self-dual because they solve first order differential equations which together with some conditions on the coupling constants, imply the second order equations of motion. The solutions belong to a sub-sector of the theory with an infinite number of local conserved currents. The equation for the profile function of the ansatz corresponds to the Bogomolny equation for the sine-Gordon model.

Super-WZNW with reductions to supersymmetric and fermionic integrable models

A systematic construction for an action describing a class of supersymmetric integrable models as well as for pure fermionic theories is discussed in terms of the gauged WZNW model associated to half integer graded affine Kac-Moody algebras. Explicit examples of the N = 1. 2 super-sinh(sine)-Gordon models are discussed in detail. Pure fermionic theories arises for cosets sl(p, 1)/sl(p) circle times u(1) when a maximal kernel condition is fulfilled. The integrability condition for such models is discussed and it is shown that the simplest example when p = 2 (cads to the constrained Bukhvostov-Lipatov, Thirring, scalar massive and pseudo-scalar massless Gross-Neveu models. (C) 2009 Published by Elsevier B.V.

Analog Model for Quantum Gravity Effects: Phonons in Random Fluids

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Flavor mixing in a Lee-type model

An exactly solvable quantum field theory (QFT) model of Lee type is constructed to study how neutrino flavor eigenstates are created through interactions and how the localization properties of neutrinos follows from the parent particle that decays. The two-particle states formed by the neutrino and the accompanying charged lepton can be calculated exactly as well as their creation probabilities. We can show that the coherent creation of neutrino flavor eigenstates follows from the common negligible contribution of neutrino masses to their creation probabilities. on the other hand, it is shown that it is not possible to associate a well-defined flavor to coherent superpositions of charged leptons.

The Unruh effect and its applications

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)