REDUCTION OF TODA LATTICE HIERARCHY TO GENERALIZED KDV HIERARCHIES AND THE 2-MATRIX MODEL

Toda lattice hierarchy and the associated matrix formulation of the 2M-boson KP hierarchies provide a framework for the Drinfeld-Sokolov reduction scheme realized through Hamiltonian action within the second KP Poisson bracket. By working with free currents, which Abelianize the second KP Hamiltonian structure, we are able to obtain a unified formalism for the reduced SL(M + 1, M - k) KdV hierarchies interpolating between the ordinary KP and KdV hierarchies. The corresponding Lax operators are given as superdeterminants of graded SL(M + 1, M - k) matrices in the diagonal gauge and we describe their bracket structure and field content. In particular, we provide explicit free field representations of the associated W(M, M - k) Poisson bracket algebras generalising the familiar nonlinear W-M+1 algebra. Discrete Backlund transformations for SL(M + 1, M - k) KdV are generated naturally from lattice translations in the underlying Toda-like hierarchy. As an application we demonstrate the equivalence of the two-matrix string model to the SL(M + 1, 1) KdV hierarchy.

Testing the principle of equivalence by supernova neutrinos

We study the possible impact of the neutrino oscillation which could be induced by a tiny violation of equivalence principle (VEP) on the observation of neutrinos emitted from supernova driven by gravitational collapse. We show that using supernova neutrinos, one can probe very small values of VEP parameters, delta(tau) less than or similar to O(10(-31)) for massless or degenerated neutrinos and delta(tau) less than or similar to O(10(-16)) x (Deltam(2)/10(-5) eV(2)) for massive neutrinos. (C) 2002 Elsevier B.V. B.V. All rights reserved.

K-bi-Lipschitz equivalence of real function-germs

In this paper we prove that the set of equivalence classes of germs of real polynomials of degree less than or equal to k, with respect to K-bi-Lipschitz equivalence, is finite.

On the equivalence of the mechanisms governing switching and hysteresis phenomena

The nucleation and growth model, which is usually applied to switching phenomena, is adapted for explaining surface potential measurements on the P(VDF-TrFE) (polyvinylidene fluoride-trifluoroethylene) copolymer obtained in a constant current corona triode. It is shown that the growth is one-dimensional and that the nucleation rate is unimportant, probably because surface potential measurements take much longer than the switching ones. The surface potential data can therefore be accounted for by a growth model in which the velocity of growth varies exponentially with the electric field. Since hysteresis loops can be obtained from surface potential measurements, it is suggested that similar mechanisms can be used when treating switching and hysteresis phenomena, provided that account is taken of the difference in the time scale of the measurements.

Constraints on singlet right-handed neutrinos coming from the Z0 width

We study the constraints on masses and mixing angles imposed by the measured Z0 invisible width, in a model in which a singlet right-handed neutrino mixes with all the standard model neutrinos. © 1993 The American Physical Society.

Remarks on fermion-boson equivalence in three dimensions

Starting from a decomposition of the self-dual field in (2 + 1) dimensions, we build up an alternative quantum theory which consists of a self-dual model coupled to a Maxwell-generalized Chern-Simons theory. We discuss the fermion-boson equivalence of this quantum theory by comparing it with the Thirring model. Using these results we were able to compute the mass of the bosonized fermions up to third order in 1/m. Some problems related to the number of poles of the effective propagator are also addressed.

Confinement, solitons and the equivalence between the sine-Gordon and massive Thirring models

We consider a two-dimensional integrable and conformally invariant field theory possessing two Dirac spinors and three scalar fields. The interaction couples bilinear terms in the spinors to exponentials of the scalars. Its integrability properties are based on the sl(2) affine Kac-Moody algebra, and it is a simple example of the so-called conformal affine Toda theories coupled to matter fields. We show, using bosonization techniques, that the classical equivalence between a U(1) Noether current and the topological current holds true at the quantum level, and then leads to a bag model like mechanism for the confinement of the spinor fields inside the solitons. By bosonizing the spinors we show that the theory decouples into a sine-Gordon model and free scalars. We construct the two-soliton solutions and show that their interactions lead to the same time delays as those for the sine-Gordon solitons. The model provides a good laboratory to test duality ideas in the context of the equivalence between the sine-Gordon and Thirring theories. © 2000 Elsevier Science B.V. All rights reserved.

Equivalence of the Duffin-Kemmer-Petiau and Klein-Gordon-Fock equations

A strict proof of the equivalence of the Duffin-Kemmer-Petiau and Klein-Gordon Fock theories is presented for physical S-matrix elements in the case of charged scalar particles minimally interacting with an external or quantized electromagnetic field. The Hamiltonian canonical approach to the Duffin - Kemmer Petiau theory is first developed in both the component and the matrix form. The theory is then quantized through the construction of the generating functional for the Green's functions, and the physical matrix elements of the S-matrix are proved to be relativistic invariants. The equivalence of the two theories is then proved for the matrix elements of the scattered scalar particles using the reduction formulas of Lehmann, Symanzik, and Zimmermann and for the many-photon Green's functions.

Classical versus quantum equivalence between sine-Gordon, Liouville and other solitons

In this work we present a mapping between the classical solutions of the sine-Gordon, Liouville, λφ4 and other kinks in 1+1 dimensions. This is done by using an invariant quantity which relates the models. It is easily shown that this procedure is equivalent to that used to get the so called deformed solitons, as proposed recently by Bazeia et al. [Phys. Rev. D. 66 (2002) 101701(R)]. The classical equivalence is explored in order to relate the solutions of the corresponding models and, as a consequence, try to get new information about them. We discuss also the difficulties and consequences which appear when one tries to extend the deformation in order to take into account the quantum version of the models.

Ghost free dual vector theories in 2 + 1 dimensions

We explore here the issue of duality versus spectrum equivalence in dual theories generated through the master action approach. Specifically we examine a generalized self-dual (GSD) model where a Maxwell term is added to the self-dual model. A gauge embedding procedure applied to the GSD model leads to a Maxwell-Chern-Simons (MCS) theory with higher derivatives. We show here that the latter contains a ghost mode contrary to the original GSD model. By figuring out the origin of the ghost we are able to suggest a new master action which interpolates between the local GSD model and a nonlocal MCS model. Those models share the same spectrum and are ghost free. Furthermore, there is a dual map between both theories at classical level which survives quantum correlation functions up to contact terms. The remarks made here may be relevant for other applications of the master action approach. © SISSA 2006.

Is the equivalence principle doomed forever to Dante's Inferno on account of quantum mechanics?

It is commonly assumed that the equivalence principle can coexist without conflict with quantum mechanics. We shall argue here that, contrary to popular belief, this principle does not hold in quantum mechanics. We illustrate this point by computing the second-order correction for the scattering of a massive scalar boson by a weak gravitational field, treated as an external field. The resulting cross-section turns out to be mass-dependent. A way out of this dilemma would be, perhaps, to consider gravitation without the equivalence principle. At first sight, this seems to be a too much drastic attitude toward general relativity. Fortunately, the teleparallel version of general relativity - a description of the gravitational interaction by a force similar to the Lorentz force of electromagnetism and that, of course, dispenses with the equivalence principle - is equivalent to general relativity, thus providing a consistent theory for gravitation in the absence of the aforementioned principle. © World Scientific Publishing Company.

Conflict between the classical equivalence principle and quantum mechanics

As far as external gravitational fields described by Newton's theory are concerned, theory shows that there is an unavoidable conflict between the universality of free fall (Galileo's equivalence principle) and quantum mechanics - a result confirmed by experiment. Is this conflict due perhaps to the use of Newton's gravity, instead of general relativity, in the analysis of the external gravitational field? The response is negative. To show this we compute the low corrections to the cross-section for the scattering of different quantum particles by an external gravitational field, treated as an external field, in the framework of Einstein's linearized gravity. To first order the cross-sections are spin-dependent; if the calculations are pushed to the next order they become dependent upon energy as well. Therefore, the Galileo's equivalence and, consequently, the classical equivalence principle, is violated in both cases. We address these issues here.

Ensino de leitura de frases com compreensão a alunos de 2ª série de escolas públicas de Belém

Estudos baseados no paradigma da equivalência de estímulos têm produzido a leitura, com compreensão, de palavras substantivas, em humanos de diferentes idades, com e sem história de fracasso escolar. O presente estudo objetivou verificar se cinco crianças, sendo quatro do sexo feminino e uma do sexo masculino, entre 8 e 11 anos, matriculadas na 2ª série do Ensino Fundamental de Escolas Públicas de BelémPA, com dificuldades em leitura, seriam capazes de aprender a ler frases às quais nunca tinham sido expostas, e se demonstravam a leitura generalizada de (novas) frases, após o ensino de pré-requisitos, no âmbito do paradigma de equivalência. Os estímulos experimentais foram sílabas, palavras e frases faladas e impressas, e figuras (relativas às palavras e frases). Foram programadas diferentes fases experimentais, envolvendo pré-testes, treinos de relações condicionais, testes de relações emergentes (equivalência e generalização), e pós-testes. Utilizou-se um formato de discriminação condicional em que o estímulo modelo (palavra, ou frase impressa, ou figura) ficava posicionado, numa cartela, sempre antes (à esquerda) dos estímulos de comparação (três palavras, ou frases impressas, ou figuras), os quais eram apresentados em posições diferentes, separados do modelo por uma linha vertical. Foram usadas instruções verbais e houve conseqüências diferenciais para acertos e erros. Exigiase do participante a obtenção de 100% de acertos no treino. Os testes, de equivalência, eram aplicados uma única vez. Nos testes de generalização, um erro implicava a reapresentação das tentativas do treino em que o responder fosse incorreto. O controle da apresentação dos estímulos, do registro das respostas e das conseqüências para acertos e para erros, e do início e término das sessões (que duravam cerca de 40 minutos), era realizado manualmente, pela experimentadora e um outro observador. Todos os participantes foram bem-sucedidos nas relações condicionais testadas e treinadas, que envolviam palavras faladas, figuras e palavras impressas correspondentes (AB e AC misto). A maioria formou a Equivalência BC relação entre figuras e respectivas palavras impressas, e todos demonstraram a relação inversa, ou a Equivalência CB. Também, os participantes nomearam as figuras correspondentes a essas palavras (BD), leram as palavras (CD) e, além disso, foram capazes de ler novas palavras (C D). Em seguida, foram bem-sucedidos nas relações condicionais entre frases faladas e figuras correspondentes (testadas e treinadas), AB e AB misto, e nas relações treinadas envolvendo frases faladas e frases impressas correspondentes (AC misto). Apenas dois participantes formaram a Equivalência BC (entre figuras e frases impressas) e a maioria formou a Equivalência CB. Também, a maioria nomeou as figuras das frases (BD), todos os participantes leram essas frases (CD), leram novas frases, organizadas pela recombinação de palavras (C D), e a maioria leu outras novas frases, organizadas pela recombinação de sílabas (C D). Um mês depois, os participantes mantiveram o desempenho na leitura das mesmas palavras, a maioria manteve a leitura das mesmas frases e a leitura generalizada das palavras e das frases novas. Este estudo possibilitou o estabelecimento de pré-requisitos para o ensino de leitura e a avaliação da compreensão, envolvendo frases simples. O estudo pode ser visto como um avanço, embora parcial, em relação aos que, tradicionalmente, têm-se fundamentado no mesmo paradigma e utilizado palavras como estímulos. É pertinente implementar novas investigações utilizando 15 unidades verbais ainda mais amplas, como frases complexas, as quais, além de conterem palavras substantivas e adjetivas, abarquem artigos, pronomes, verbos, advérbios, etc.

Translation and cultural adaptation of Brazilian Detailed Assessment of Speed of Handwriting: conceptual and semantic equivalence

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

Corroborating the equivalence between the Duffin-Kemmer-Petiau and the Klein-Gordon and Proca equations

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)