Field-theory Two-point Functions via Negative Dimension Integration

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Comment on Wave functions for a Duffin-Kemmer-Petiau particle in a time-dependent potential [J. Math. Phys. 48, 073515 (2007)]

It is shown that the paper Wave functions for a Duffin-Kemmer-Petiau particle in a time-dependent potential by Merad and Bensaid [J. Math. Phys. 48, 073515 (2007)] is not correct in using inadvertently a non-Hermitian Hamiltonian in a formalism that does require Hermitian Hamiltonians.

Analytical optimization of spread and change of exponential decay of generalized Wannier functions in one dimension

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

GENERALIZED HEAVISIDE FUNCTIONS IN THE COLOMBEAU THEORY CONTEXT

We defined generalized Heaviside functions for a variable x in R-n, and for variables (x, t) in R-n x R-m. Then study properties such as: composition, invertibility, and association relation (the weak equality). This work is developed in the Colombeau generalized functions context.

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.

Correlation functions in super liouville theory

We calculate three- and four-point functions in super Liouville theory coupled to a super Coulomb gas on world sheets with spherical topology. We first integrate over the zero mode and assume that a parameter takes an integer value. We find the amplitudes, give plausibility arguments in favor of the result, and formally continue the parameter to an arbitrary real number. Remarkably the result is completely parallel to the bosonic case.

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.