Vertex operators and soliton solutions of affine Toda model with U(2) symmetry

The symmetry structure of the non-Abelian affine Toda model based on the coset SL(3)/SL(2) circle times U(1) is studied. It is shown that the model possess non-Abelian Noether symmetry closing into a q-deformed SL(2) circle times U(1) algebra. Specific two-vertex soliton solutions are constructed.

Pure spinor vertex operators in Siegel gauge and loop amplitude regularization

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

Generalized squeezing operators, bipartite Wigner functions and entanglement via Wehrl's entropy functionals

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A new proposal for the picture changing operators in the minimal pure spinor formalism

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

New class of spin projection operators for 3D models

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Effects of oscillatory behavior of the dipole function on the dissociation dynamics of the classical driven Morse oscillator

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

An algebraic q-deformed form for shape-invariant systems

A quantum deformed theory applicable to all shape-invariant bound-state systems is introduced by defining q-deformed ladder operators. We show that these new ladder operators satisfy new q-deformed commutation relations. In this context we construct an alternative q-deformed model that preserves the shape-invariance property presented by the primary system. q-deformed generalizations of Morse, Scarf and Coulomb potentials are given as examples.

Ladder operators for subtle hidden shape-invariant potentials

Ladder operators can be constructed for all potentials that present the integrability condition known as shape invariance, satisfied by most of the exactly solvable potentials. Using the superalgebra of supersymmetric quantum mechanics, we construct the ladder operators for two exactly solvable potentials that present a subtle hidden shape invariance.

Comments on spin operators and spin-polarization states of 2+1 fermions

In this brief article we discuss spin-polarization operators and spin-polarization states of 2 + 1 massive Dirac fermions and find a convenient representation by the help of 4-spinors for their description. We stress that in particular the use of such a representation allows us to introduce the conserved covariant spin operator in the 2 + 1 field theory. Another advantage of this representation is related to the pseudoclassical limit of the theory. Indeed, quantization of the pseudoclassical model of a spinning particle in 2 + 1 dimensions leads to the 4-spinor representation as the adequate realization of the operator algebra, where the corresponding operator of a first-class constraint, which cannot be gauged out by imposing the gauge condition, is just the covariant operator previously introduced in the quantum theory.

Dynamics in discrete phase spaces and time interval operators

The von Neumann-Liouville time evolution equation is represented in a discrete quantum phase space. The mapped Liouville operator and the corresponding Wigner function are explicitly written for the problem of a magnetic moment interacting with a magnetic field and the precessing solution is found. The propagator is also discussed and a time interval operator, associated to a unitary operator which shifts the energy levels in the Zeeman spectrum, is introduced. This operator is associated to the particular dynamical process and is not the continuous parameter describing the time evolution. The pair of unitary operators which shifts the time and energy is shown to obey the Weyl-Schwinger algebra. (C) 1999 Elsevier B.V. B.V. All rights reserved.

Morse basis expansion applied to diatomic molecules

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

Vertex operators and Jordan fields

The construction of Lie algebras in terms of Jordan algebra generators is discussed. The key to the construction is the triality relation already incorporated into matrix products. A generalisation to Kac-Moody algebras in terms of vertex operators is proposed and may provide a clue for the construction of new representations of Kac-Moody algebras in terms of Jordan fields. © 1988.

Conservation laws for non-potential operators

A study was developed in order to build a function M invariant in time, by means of Hamiltonian's formulation, taking into account the equation associated to the problem, showing that starting from this function the equation of motion of the system with the contour conditions for non-conservative considered problems can be obtained. The Hamiltonian method is extended for these kind of systems in order to validate for non-potential operators through variational approach.

Morse potential energy spectra through the variational method and supersymmetry

The Variational Method is applied within the context of Supersymmetric Quantum Mechanics to provide information about the energy and eigenfunction of the lowest levels of a Hamiltonian. The approach is illustrated by the case of the Morse potential applied to several diatomic molecules and the results are compared with stabilished results. (C) 2000 Elsevier Science B.V.