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Complex Boosts: A Hermitian Clifford Algebra Approach
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Orientador(es)
Resumo(s)
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.
Descrição
Palavras-chave
Pseudo-unitary group Complex boosts Hermitian Clifford algebra Complex Einstein velocity addition
Contexto Educativo
Citação
Ferreira, M., and Sommen, F., Complex boosts: a Hermitian Clifford algebra approach, Adv. Appl. Clifford Algebras, 23(2), 2013, 339-362
Editora
Springer Nature [academic journals on nature.com]