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Projeto de investigação
Strategic Project - UI 4106 - 2011-2012
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Publicações
Complex Boosts: A Hermitian Clifford Algebra Approach
Publication . Ferreira, Milton; Sommen, Franciscus
The aim of this paper is to study complex boosts in complex Minkowski space-time that preserves the Hermitian norm. Starting from the spin group Spin$^+(2n,2m,\bkR)$ in the real Minkowski space $\bkR^{2n,2m}$ we construct a Clifford realization of the pseudo-unitary group U$(n,m)$ using the space-time Witt basis in the framework of Hermitian Clifford algebra. Restricting to the case of one complex time direction we derive a general formula for a complex boost in an arbitrary complex direction and its $KAK-$decomposition, generalizing the well-known formula of a real boost in an arbitrary real direction. In the end we derive the complex Einstein velocity addition law for complex relativistic velocities, by the projective model of hyperbolic $n-$space.
3D deformations by means of monogenic functions
Publication . Ferreira, Milton; Morais, João
In this paper, the authors compute the coefficient of quasiconformality for monogenic functions in an arbitrary ball of the Euclidean space $\mathbb{R}^3$. This quantification may be needed in applications but also appear to be of intrinsic interest. The main tool used is a 3D Fourier series development of monogenic functions in terms of a special set of solid spherical monogenics. Ultimately, we present some examples showing the applicability of our approach.
Multidimensional fractional Schrödinger equation
Publication . Rodrigues, M. M.; Vieira, Nelson
This work is intended to investigate the multi-dimensional space-time fractional Schrödinger equation of the form ħ𝛻 , with ħ the Planck's constant divided by 2π, m is the mass and u(t,x) is a wave function of the particle. Here 𝛻 are operators of the Caputo fractional derivatives, where α ∈]0,1] and β ∈]1,2]. The wave function is obtained using Laplace and Fourier transforms methods and a symbolic operational form of solutions in terms of the Mittag-Leffler functions is exhibited. It is presented an expression for the wave function and for the quantum mechanical probability density. Using Banach fixed point theorem, the existence and uniqueness of solutions is studied for this kind of fractional differential equations.
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Entidade financiadora
Fundação para a Ciência e a Tecnologia
Programa de financiamento
6820 - DCRRNI ID
Número da atribuição
PEst-C/MAT/UI4106/2011