Unitary Operator Bases and Q-deformed Algebras

Starting from the Schwinger unitary operator bases formalism constructed out of a finite dimensional state space, the well-known q-deformed commutation relation is shown to emerge in a natural way, when the deformation parameter is a root of unity.

An extended Weyl-Wigner transformation for special finite spaces

We extend the Weyl-Wigner transformation to those particular degrees of freedom described by a finite number of states using a technique of constructing operator bases developed by Schwinger. Discrete transformation kernels are presented instead of continuous coordinate-momentum pair system and systems such as the one-dimensional canonical continuous coordinate-momentum pair system and the two-dimensional rotation system are described by special limits. Expressions are explicitly given for the spin one-half case. © 1988.

Quantum discrete phase space dynamics and its continuous limit

The main aspects of a discrete phase space formalism are presented and the discrete dynamical bracket, suitable for the description of time evolution in finite-dimensional spaces, is discussed. A set of operator bases is defined in such a way that the Weyl-Wigner formalism is shown to be obtained as a limiting case. In the same form, the Moyal bracket is shown to be the limiting case of the discrete dynamical bracket. The dynamics in quantum discrete phase spaces is shown not to be attained from discretization of the continuous case.

QUASIDISTRIBUTIONS and COHERENT STATES FOR FINITE-DIMENSIONAL QUANTUM SYSTEMS

In recent years, an approach to discrete quantum phase spaces which comprehends all the main quasiprobability distributions known has been developed. It is the research that started with the pioneering work of Galetti and Piza, where the idea of operator bases constructed of discrete Fourier transforms of unitary displacement operators was first introduced. Subsequently, the discrete coherent states were introduced, and finally, the s-parametrized distributions, that include the Wigner, Husimi, and Glauber-Sudarshan distribution functions as particular cases. In the present work, we adapt its formulation to encompass some additional discrete symmetries, achieving an elegant yet physically sound formalism.

Discrete coherent states and probability distributions in finite-dimensional spaces

Operator bases are discussed in connection with the construction of phase space representatives of operators in finite-dimensional spaces, and their properties are presented. It is also shown how these operator bases allow for the construction of a finite harmonic oscillator-like coherent state. Creation and annihilation operators for the Fock finite-dimensional space are discussed and their expressions in terms of the operator bases are explicitly written. The relevant finite-dimensional probability distributions are obtained and their limiting behavior for an infinite-dimensional space are calculated which agree with the well known results. (C) 1996 Academic Press, Inc.

PATH INTEGRAL AND OPERATOR APPROACH FOR THE PODOLSKY-SCHWINGER MODEL

We study the role of the thachyonic excitation which emerges from the quantum electrodynamics in two dimensions with Podolsky term. The quantization is performed by using path integral framework and the operator approach.

HIGHER-DERIVATIVE SCHWINGER MODEL

Using the operator formalism, we obtain the bosonic representation for the free fermion field satisfying an equation of motion with higher-order derivatives. Then, we consider the operator solution of a generalized Schwinger model with higher-derivative coupling. Since the increasing of the derivative order implies the introduction of an equivalent number of extra fermionic degrees of freedom, the mass acquired by the gauge field is bigger than the one for the standard two-dimensional QED. An analysis of the problem from the functional integration point of view corroborates the findings of canonical quantization, and corrects certain results previously announced in the literature on the basis of Fujikawa's technique.

O princípio de ação quântica de Schwinger: aspectos do tratamento de sistemas dependentes do tempo e interagentes

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Acupuntura: bases científicas e aplicações

A acupuntura visa à terapia e à cura das enfermidades pela aplicação de estímulos através da pele, com a inserção de agulhas em pontos específicos. Essa técnica esteve isolada do mundo ocidental durante milênios, distanciando sua forma de raciocínio e linguagem da cultura ocidental. Isto restringe sua aceitação no Ocidente, sendo considerada mística e sem base científica. Além disso, a prática da acupuntura no Ocidente se depara com deficiências no ensino e difusão científica. Porém, a eficácia dessa terapia levou a Organização Mundial de Saúde a listar enfermidades que podem ser tratadas pela acupuntura e, recentemente, essa técnica foi reconhecida como especialidade médica veterinária no Brasil. A pesquisa da acupuntura reveste-se, portanto, de grande interesse, na medida em que poderá traduzir conhecimentos milenares, contribuindo para sua aceitação e incorporação.

Effect of wounds applied to the bases of herbaceous cuttings on the rooting of four Japanese apricot clones (Prunus mume Sieb. et Zucc.) in an intermittent mist system

The Japanese apricot (Prunus mume Sieb. et Zucc.) is a fruit tree of the Rosaceae family which produces very acid and bitter fruits, highly appreciated by Orientals. In Brazil, this species has been studied as a rootstock for peach and nectarine trees, its main advantage being the reduction in plant vigour, which can favour the production of compact trees and orchard cultural treatments. This study was conducted in the Vegetable Production Department of FCAV/UNESP, Jaboticabal Campus, São Paulo State, Brazil, and the objective was to examine the effect of wounding the herbaceous cutting bases on the rooting of four Japanese apricot clones. The clones were obtained from plants under cultivation in the Instituto Agronomico de Campinas, Brazil, and were identified as Clones 02, 05, 10 and 15. The stock plants, obtained through herbaceous cuttings, were maintained under lath house conditions (50% of natural light). Cuttings 12 cm long with 3 to 5 leaves were collected from these clones and prepared. The experiment was carried out in a completely randomised design with 4 repetitions of 20 cuttings per replication, in a factorial 4 x 2 design, the clone factor having 4 levels (Clones 02, 05, 10 and 15) and the wounding factor at 2 levels of incisions into the cutting base (with and without). All the cuttings were treated with 2000 mg.L-1 of IBA for five seconds. Differences between the clones were observed concerning the rooting percentage, dead cuttings, number and length of roots. The incision (wound) at the base of the herbaceous cuttings of the Japanese apricot increased the number of roots and improved the distribution of these in the damaged tissue but the results were not considered sufficiently beneficial to make the treatment worthwhile.

Bases para a padronização do teste de germinação em três espécies de Solanum L.

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

Produção de matéria seca e absorção de nutrientes pelo milho em razão da saturação por bases e da adubação potássica

O trabalho foi conduzido em condições de casa de vegetação, com o objetivo de avaliar a resposta do milho à adubação potássica e à saturação do solo por bases, na produção de matéria seca e na absorção de nutrientes. O delineamento experimental foi inteiramente casualizado, com quatro repetições, em esquema fatorial 3x2x4, constituindo-se de três solos (Areia Quartzosa, Latossolo Vermelho-Escuro e Latossolo Roxo), dois valores de saturação por bases (40% e 70 %) e quatro teores de K no solo (0,5, 1,5, 3,0 e 6,0 mmol c dm-3). Para a calagem, foi utilizada mistura de carbonato de cálcio + carbonato de magnésio (PRNT = 103,3 %) na proporção de 4:1. A adubação básica constou de 200 mg kg-1 de N, 200 mg kg-1 de P e 5 mg kg-1 de Zn por vaso de 30 L, sendo o N parcelado em 2,48 g (83,7 mg kg-1) na semeadura e o restante em duas coberturas aos 25 e 40 dias após a emergência das plântulas (DAE). As doses de K utilizadas foram de 0, 3,62, 7,24 e 14,48 g de KCl por vaso. A semeadura foi realizada em 4/3/97, utilizando-se o milho cv. Zêneca 8392, mantendo-se uma planta/vaso durante 60 DAE. O K proporciona ganhos de matéria seca até teores de 1,5 mmol c dm-3 no solo. O aumento dos teores de K no solo resultam em queda na concentração de Ca e Mg na matéria seca do milho. A elevação da saturação por bases e respectivo aumento dos teores de Ca e Mg no solo reduzem a absorção de K pelo milho.

Crescimento do milho em função da saturação por bases e da adubação potássica

Os teores de Ca, Mg e K no solo interferem no crescimento e na produção das culturas. No entanto, a relação entre esses nutrientes que proporciona o desenvolvimento adequado das plantas varia entre as espécies vegetais. O presente teve por objetivo estudar o desenvolvimento do milho em função da saturação do solo por bases e adubação potássica. O delineamento experimental foi inteiramente casualizado, com quatro repetições, em esquema fatorial 3x2x4, constituindo-se de três solos (Neossolo Quartzarênico, Latossolo Vermelho e Latossolo Bruno), dois valores de saturação por bases (40 e 70 %) e quatro doses de potássio no solo (0, 60, 120 e 240 mg kg-1). O experimento foi conduzido em casa-de-vegetação, utilizando-se o milho cv. Zêneca 8392 com uma planta por vaso de 30 L. Aos 29, 57 e 127 dias após a emergência das plântulas, efetuaram-se medidas do número de folhas por planta, altura média das plantas, diâmetro basal do colmo e comprimento médio de entrenós. Após a colheita final determinou-se a produção de grãos por planta. O desenvolvimento e a produção de grãos do milho aumentou até a adição de 60 mg kg-1 de K ao solo. O crescimento do milho foi mais rápido no solo mais arenoso, até o florescimento masculino. Solos com maior capacidade de troca catiônica proporcionaram maior comprimento de entrenós. O comprimento médio de entrenós foi inversamente relacionado ao número médio de entrenós por planta, em função do tipo de solo.

Níveis crescentes de saturação por bases e desenvolvimento inicial de teca em um latossolo de textura média

Teak is a forest species of high commercial value, but the little knowledge on the behavior of this species in relation to soil acidity is an important factor that may limit its cultivation. The aim of this study was to evaluate the effect of high base saturation on the soil on the initial development of teak (Tectona grandis L.f.). The experiment was conducted in a greenhouse, in plastic containers with capacity of 50 liters. The experimental design was randomized, with five treatments and four replications. The treatments consisted of: natural saturation of the soil and the other treatments with 20 %, 40 %, 60 % and 80 % of saturation. Correcting the soil favored the growth characteristics of all evaluated plant teak. The liming positively affected the uptake of N, P, K, Ca, Mg, B, Cu and Fe, and the nutritional requirements of the species had the following order: N > Ca > K > Mg > P > S > Fe > Mn > B > Zn > Cu. Base saturations above 70 % showed higher plant development.

Selectivity of the cyclic carbonate formation by fixation of carbon dioxide into epoxides catalyzed by Lewis bases

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