A discrete finite-dimensional phase space approach for the description of Fe8 magnetic clusters: Wigner and Husimi functions

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Path integral quantization of generalized quantum electrodynamics

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On the hardy space H¹ on products of half-spaces

We show that the Hardy space H¹ anal (R2+ x R2+) can be identified with the class of functions f such that f and all its double and partial Hubert transforms Hk f belong to L¹ (R2). A basic tool used in the proof is the bisubharmonicity of |F|q, where F is a vector field that satisfies a generalized conjugate system of Cauchy-Riemann type.

COMPARISON OF THE ANOMALOUS AND NONANOMALOUS GENERALIZED SCHWINGER MODELS VIA THE FUNCTIONAL FORMALISM

We calculate the Green functions of the two versions of the generalized Schwinger model, the anomalous and the nonanomalous one, in their higher order Lagrangian density form. Furthermore, it is shown through a sequence of transformations that the bosonized Lagrangian density is equivalent to the former, at least for the bosonic correlation functions. The introduction of the sources from the beginning, leading to a gauge-invariant source term, is also considered. It is verified that the two models have the same correlation functions only if the gauge-invariant sector is taken into account. Finally, there is presented a generalization of the Wess-Zumino term, and its physical consequences are studied, in particular the appearance of gauge-dependent massive excitations.

Integration of polyharmonic functions

The results in this paper are motivated by two analogies. First, m-harmonic functions in R(n) are extensions of the univariate algebraic polynomials of odd degree 2m-1. Second, Gauss' and Pizzetti's mean value formulae are natural multivariate analogues of the rectangular and Taylor's quadrature formulae, respectively. This point of view suggests that some theorems concerning quadrature rules could be generalized to results about integration of polyharmonic functions. This is done for the Tchakaloff-Obrechkoff quadrature formula and for the Gaussian quadrature with two nodes.

Solitons, τ-functions and hamiltonian reduction for non-Abelian conformal affine Toda theories

We consider the Hamiltonian reduction of the two-loop Wess-Zumino-Novikov-Witten model (WZNW) based on an untwisted affine Kac-Moody algebra script Ĝ. The resulting reduced models, called Generalized Non-Abelian Conformal Affine Toda (G-CAT), are conformally invariant and a wide class of them possesses soliton solutions; these models constitute non-Abelian generalizations of the conformal affine Toda models. Their general solution is constructed by the Leznov-Saveliev method. Moreover, the dressing transformations leading to the solutions in the orbit of the vacuum are considered in detail, as well as the τ-functions, which are defined for any integrable highest weight representation of script Ĝ, irrespectively of its particular realization. When the conformal symmetry is spontaneously broken, the G-CAT model becomes a generalized affine Toda model, whose soliton solutions are constructed. Their masses are obtained exploring the spontaneous breakdown of the conformal symmetry, and their relation to the fundamental particle masses is discussed. We also introduce what we call the two-loop Virasoro algebra, describing extended symmetries of the two-loop WZNW models.

Kinetics of the polarization reversal process in a non-constant applied electric field and the generalized superposition principle

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Tau-functions and dressing transformations for zero-curvature affine integrable equations

The solutions of a large class of hierarchies of zero-curvature equations that includes Toda- and KdV-type hierarchies are investigated. All these hierarchies are constructed from affine (twisted or untwisted) Kac-Moody algebras g. Their common feature is that they have some special vacuum solutions corresponding to Lax operators lying in some Abelian (up to the central term) subalgebra of g; in some interesting cases such subalgebras are of the Heisenberg type. Using the dressing transformation method, the solutions in the orbit of those vacuum solutions are constructed in a uniform way. Then, the generalized tau-functions for those hierarchies are defined as an alternative set of variables corresponding to certain matrix elements evaluated in the integrable highest-weight representations of g. Such definition of tau-functions applies for any level of the representation, and it is independent of its realization (vertex operator or not). The particular important cases of generalized mKdV and KdV hierarchies as well as the Abelian and non-Abelian affine Toda theories are discussed in detail. © 1997 American Institute of Physics.

Extended Hierarchical Censored Production Rules (EHCPRs) system: An approach toward generalized knowledge representation

One common problem in all basic techniques of knowledge representation is the handling of the trade-off between precision of inferences and resource constraints, such as time and memory. Michalski and Winston (1986) suggested the Censored Production Rule (CPR) as an underlying representation and computational mechanism to enable logic based systems to exhibit variable precision in which certainty varies while specificity stays constant. As an extension of CPR, the Hierarchical Censored Production Rules (HCPRs) system of knowledge representation, proposed by Bharadwaj & Jain (1992), exhibits both variable certainty as well as variable specificity and offers mechanisms for handling the trade-off between the two. An HCPR has the form: Decision If(preconditions) Unless(censor) Generality(general_information) Specificity(specific_information). As an attempt towards evolving a generalized knowledge representation, an Extended Hierarchical Censored Production Rules (EHCPRs) system is suggested in this paper. With the inclusion of new operators, an Extended Hierarchical Censored Production Rule (EHCPR) takes the general form: Concept If (Preconditions) Unless (Exceptions) Generality (General-Concept) Specificity (Specific Concepts) Has_part (default: structural-parts) Has_property (default:characteristic-properties) Has_instance (instances). How semantic networks and frames are represented in terms of an EHCPRs is shown. Multiple inheritance, inheritance with and without cancellation, recognition with partial match, and a few default logic problems are shown to be tackled efficiently in the proposed system.

Class of self-dual models in three dimensions

In the present paper we introduce a hierarchical class of self-dual models in three dimensions, inspired in the original self-dual theory of Towsend-Pilch-Nieuwenhuizen. The basic strategy is to explore the powerful property of the duality transformations in order to generate a new field. The generalized propagator can be written in terms of the primitive one (first order), and also the respective order and disorder correlation functions. Some conclusions about the charge screening and magnetic flux were established. ©1999 The American Physical Society.

Electromyographic validation of basic exercises for physical conditioning programmes V. The comparison of the response in the deltoid muscle (anterior portion) and the pectoralis major muscle (clavicular portion) determined by the frontal-lateral cross, dumbbells and the rowing exercises

The action potential level for shoulder muscles deltoid-anterior portion (DA) and pectoralis major-clavicular portion (PMC) determined by four different modalities of execution of rowing exercises, each one with two different grips, was recorded. These were compared with the action potential level determined for the same muscles by four different modalities of execution of the frontal-lateral cross, dumbbells exercises. Twenty-four male volunteers were examined using a 2 channel TECA TE4 electromyograph and Hewlett Packard surface electrodes. The statistic analysis showed significant (p<0,05) superiority for all the frontal-lateral cross, dumbbells exercises in comparison to all rowing exercises for the PMC, for the DA this generalized supremacy was not observed.

Classes of exact wave functions for general time-dependent Dirac Hamiltonians in 1+1 dimensions

The construction of two classes of exact solutions for the most general time-dependent Dirac Hamiltonian in 1+1 dimensions was discussed. The extension of solutions by introduction of a time-dependent mass was elaborated. The possibility of existence of a generalized Lewis-Riesenfeld invariant connected with such solutions was also analyzed.

Batalin-Fradkin-Vilkovisky quantization of the generalized scalar electrodynamics

This work comprises a study upon the quantization and the renormalizability of the generalized electrodynamics of spinless charged particles (mesons), namely, the generalized scalar electrodynamics (GSQED4). The theory is quantized in the covariant framework of the Batalin-Fradkin-Vilkovisky method. Thereafter, the complete Green's functions are obtained through functional methods and a proper discussion on the theory's renormalizability is also given. Next, we present the computation and further discussion on the radiative correction at α order; and, as it turns out, an unexpected mP-dependent divergence on the mesonic sector of the theory is found. Furthermore, in order to show the effectiveness of the renormalization procedure on the present theory, we also give a diagrammatic discussion on the photon self-energy at α2 order, where we observe contributions from the meson self-energy function. Afterwards, we present the expressions of the counterterms and effective coupling of the theory, obtaining from the latter an energy range where the theory is defined by m2≤k2

Cálculos de integrais de Feynman em teorias de campos

Pós-graduação em Física - IFT

Stieltjes functions and discrete classical orthogonal polynomials

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)