Strategic Project - UI 4106 - 2011-2012

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Publications

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.

2013-06Journal article

Open access

3D deformations by means of monogenic functions

Publication . Morais, João; Ferreira, Milton

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.

2013-04Journal article

Open access