The Dirac equation in a non-Riemannian manifold. I. An analysis using the complex algebra

The Dirac wave equation is obtained in the non-Riemannian manifold of the Einstein-Schrödinger nonsymmetric theory. A new internal connection is determined in terms of complex vierbeins, which shows the coupling of the electromagnetic potential with gravity in the presence of a spin-1/2 field. © 1988 American Institute of Physics.

Higher spin symmetries and w∞ algebra in the conformal affine Toda model

As recently shown the conformal affine Toda models can be obtained via hamiltonian reduction from a two-loop Kac-Moody algebra. In this paper we propose a systematic procedure to analyze the higher spin symmetries of the conformal affine Toda models. The method is based on an explicit construction of infinite towers of extended conformal symmetry generators. Two fundamental building blocks of this construction are special spin-one and -two primary fields characterizing the conformal structure of these models. The connection to the algebra of area preserving diffeomorphisms on a two-manifold (w∞ algebra) is established.

Further on the current algebra of WZNW models at and away from criticality

We comment on the off-critical perturbations of WZNW models by a mass term as well as by another descendent operator, when we can compare the results with further algebra obtained from the Dirac quantization of the model, in such a way that a more general class of models be included. We discover, in both cases, hidden Kac-Moody algebras obeyed by some currents in the off-critical case, which in several cases are enough to completely fix the correlation functions.

So(2,1) Lie algebra and the Green's functions for the conditionally exactly solvable potentials

The Green's functions of the recently discovered conditionally exactly solvable potentials are computed. This is done through the use of a second-order differential realization of the so(2,1) Lie algebra. So we present the dynamical symmetry underlying the solvability of such potentials and show that they belong to a general class of solvable and partially solvable potentials. © 1994 The American Physical Society.

A free relativistic anyon with canonical spin algebra

We discuss a relativistic free particle with fractional spin in 2+1 dimensions, where the dual spin components satisfy the canonical angular momentum algebra {Sμ, Sν} = εμνγSγ. It is shown that it is a general consequence of these features that the Poincaré invariance is broken down to the Lorentz one, so indicating that it is not possible to keep simultaneously the free nature of the anyon and the translational invariance.

Closed expressions for Lie algebra invariants and finite transformations

A simple procedure to obtain complete, closed expressions for Lie algebra invariants is presented. The invariants are ultimately polynomials in the group parameters. The construction of finite group elements requires the use of projectors, whose coefficients are invariant polynomials. The detailed general forms of these projectors are given. Closed expressions for finite Lorentz transformations, both homogeneous and inhomogeneous, as well as for Galilei transformations, are found as examples.

Ramond-ramond central charges in the supersymmetry algebra of the superstring

The free action for the massless sector of the type II superstring was recently constructed using closed Ramond-Neveo-Schwarz superstring field theory. The supersymmetry transformations of this action are shown to satisfy an N = 2 D = 10 supersymmetry algebra with Ramond-Ramond central charges.

Hamiltonian reduction and the construction of q-deformed extensions of the Virasoro algebra

In this paper we employ the construction of the Dirac bracket for the remaining current of sl(2) q deformed Kac-Moody algebra when constraints similar to those connecting the sl(2)-Wess-Zumino-Witten model and the Liouville theory are imposed to show that it satisfies the q-Virasoro algebra proposed by Frenkel and Reshetikhin The crucial assumption considered in our calculation is the existence of a classical Poisson bracket algebra induced in a consistent manner by the correspondence principle, mapping the quantum generators into commuting objects of classical nature preserving their algebra.

Optimality conditions for pareto nonsmooth nonconvex programming in banach spaces

In this paper, we consider a vector optimization problem where all functions involved are defined on Banach spaces. We obtain necessary and sufficient criteria for optimality in the form of Karush-Kuhn-Tucker conditions. We also introduce a nonsmooth dual problem and provide duality theorems.

Composition for a class of generalized functions in Colombeau's theory

In Colombeau's theory, given an open subset Ω of ℝn, there is a differential algebra G(Ω) of generalized functions which contains in a natural way the space D′(Ω) of distributions as a vector subspace. There is also a simpler version of the algebra G,(Ω). Although this subalgebra does not contain, in canonical way, the space D′(Ω) is enough for most applications. This work is developed in the simplified generalized functions framework. In several applications it is necessary to compute higher intrinsic derivatives of generalized functions, and since these derivatives are multilinear maps, it is necessary to define the space of generalized functions in Banach spaces. In this article we introduce the composite function for a special class of generalized mappings (defined in open subsets of Banach spaces with values in Banach spaces) and we compute the higher intrinsic derivative of this composite function.

Quasiconformal mappings in octonionic algebra: A graphical and analytical comparison

In this article, we present quasiconformal mappings related to octonionic algebra. Based on the metric definition of quasiconformal mappings and using transformations of the type f(z)=zn, we compare the graphical and analytic results. © 2009 Pushpa Publishing House.

Optimal clone identifier based on dynamic rules and process algebra

The rule creation to clone selection in different projects is a hard task to perform by using traditional implementations to control all the processes of the system. The use of an algebraic language is an alternative approach to manage all of system flow in a flexible way. In order to increase the power of versatility and consistency in defining the rules for optimal clone selection, this paper presents the software OCI 2 in which uses process algebra in the flow behavior of the system. OCI 2, controlled by an algebraic approach was applied in the rules elaboration for clone selection containing unique genes in the partial genome of the bacterium Bradyrhizobium elkanii Semia 587 and in the whole genome of the bacterium Xanthomonas axonopodis pv. citri. Copyright© (2009) by the International Society for Research in Science and Technology.

Algebra

Incluye Bibliografía

Existência de solução de equações integrais não lineares em escalas temporais sobre espaços de Banach

Pós-graduação em Matemática - IBILCE