Advances in Applied Clifford Algebras

, Volume 23, Issue 2, pp 339–362 | Cite as

Complex Boosts: A Hermitian Clifford Algebra Approach

  • Milton FerreiraEmail author
  • Frank Sommen


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\({^+(2n, 2m, \mathbb{R})}\) in the real Minkowski space \({\mathbb{R}^{2n,2m}}\) 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.


Pseudo-unitary group complex boosts Hermitian Clifford algebra Complex Einstein velocity addition 


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© Springer Basel 2012

Authors and Affiliations

  1. 1.School of Technology and ManagementPolytechnical Institute of LeiriaLeiriaPortugal
  2. 2.Center for Research and Development in Mathematics and ApplicationsDepartment of MathematicsUniversity of AveiroAveiroPortugal
  3. 3.Department of Mathematical AnalyisClifford Research Group, Ghent UniversityGhentBelgium

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