A class of soliton solutions for the N=2 super mKdV/Sinh-Gordon hierarchy

Employing Hirota's method, a class of soliton solutions for the N = 2 super mKdV equations is proposed in terms of a single Grassmann parameter. Such solutions are shown to satisfy two copies of N = 1 supersymmetric mKdV equations connected by nontrivial algebraic identities. Using the super Miura transformation, we obtain solutions of the N = 2 super KdV equations. These are shown to generalize solutions derived previously. By using them KdV/sinh-Gordon hierarchy properties we generate the solutions of the N = 2 super sinh-Gordon as well.

Permutability of Backlund transformation for N=1 supersymmetric sinh-Gordon

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Integrablility of a classical N=2 super sinh-Gordon model with jump defects

The Lagrangian formalism for the N = 2 supersymmetric sinh-Gordon model with a jump defect is considered. The modified conserved momentum and energy are constructed in terms of border functions. The supersymmetric Backlund transformation is given and an one-soliton solution is obtained.The Lax formulation based on the affine super Lie algebra sl(2, 2) within the space split by the defect leads to the integrability of the model and henceforth to the existence of an infinite number of constants of motion.

Classical integrable N=1 and N=2 super sinh-Gordon models with jump defects

The structure of integrable field theories in the presence of jump defects is discussed in terms of boundary functions under the Lagrangian formalism. Explicit examples of bosonic and fermionic theories are considered. In particular, the boundary functions for the N = 1 and N = 2 super sinh-Gordon models are constructed and shown to generate the Backlund transformations for its soliton solutions. As a new and interesting example, a solution with an incoming boson and an outgoing fermion for the N = 1 case is presented. The resulting integrable models are shown to be invariant under supersymmetric transformation.

Classes of exact Klein-Gordon equations with spatially dependent masses: Regularizing the one-dimensional inversely linear potential

In this work we consider the effect of a spatially dependent mass over the solution of the Klein-Gordon equation in 1 + 1 dimensions, particularly the case of inversely linear scalar potential, which usually presents problems of divergence of the ground-state wave function at the origin, and possible nonexistence of the even-parity wave functions. Here we study this problem, showing that for a certain dependence of the mass with respect to the coordinate, this problem disappears. (c) 2006 Elsevier B.V. All rights reserved.

Equivalence of many-gluon Green's functions in the Duffin-Kemmer-Petieu and Klein-Gordon-Fock statistical quantum field theories

We prove the equivalence of many-gluon Green's functions in the Duffin-Kemmer-Petieu and Klein-Gordon-Fock statistical quantum field theories. The proof is based on the functional integral formulation for the statistical generating functional in a finite-temperature quantum field theory. As an illustration, we calculate one-loop polarization operators in both theories and show that their expressions indeed coincide.

On some classes of exactly-solvable Klein-Gordon equations

In this work we discuss some exactly solvable Klein-Gordon equations. We basically discuss the existence of classes of potentials with different nonrelativistic limits, but which shares the intermediate effective Schroedinger differential equation. We comment about the possible use of relativistic exact solutions as approximations for nonrelativistic inexact potentials. (c) 2005 Elsevier 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.

An extremal nonnegative sine polynomial

For any positive integer n, the sine polynomials that are nonnegative in [0, π] and which have the maximal derivative at the origin are determined in an explicit form. Associated cosine polynomials Kn (θ) are constructed in such a way that {Kn(θ)} is a summability kernel. Thus, for each Pi 1 ≤ P ≤ ∞ and for any 27π-periodic function f ∈ Lp [-π, π], the sequence of convolutions Kn * f is proved to converge to f in Lp[-ππ]. The pointwise and almost everywhere convergences are also consequences of our construction.

Sobre interações escalares e vetoriais na teoria de Duffin-Kemmer-Petiau

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Hierarquia mKdV e sinh-Gordon supersimétrica com N = 1

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Operador quaterniônico de Klein-Gordon-Dirac

Pós-graduação em Matemática - IBILCE

Estudo da equação de Klein-Gordon linear

Pós-graduação em Matemática - IBILCE

Argumentos de Gordon no estudo espectral de operadores de Schrödinger unidimensionais

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)