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Article Dans Une Revue Advances in Applied Clifford Algebras Année : 2021

Dual Hyperquaternion Poincaré Groups

Résumé

A new representation of the Poincaré groups in n dimensions via dual hyperquaternions is developed, hyperquaternions being defined as a tensor product of quaternion algebras (or a subalgebra thereof). This formalism yields a uniquely defined product and simple expressions of the Poincaré generators, with immediate physical meaning, revealing the algebraic structure independently of matrices or operators. An extended multivector calculus is introduced (allowing a possible sign change of the metric or of the exterior product). The Poincaré groups are formulated as a dual extension of hyperquaternion pseudo-orthogonal groups. The canonical decomposition and the invariants are discussed. As concrete example, the 4D Poincaré group is examined together with a numerical application. Finally, the hyperquaternion representation is compared to the quantum mechanical one. Potential applications include in particular, moving reference frames and computer graphics.
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Dates et versions

hal-03139597 , version 1 (28-11-2021)

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Patrick R. Girard, Patrick Clarysse, Romaric Pujol, Robert Goutte, Philippe Delachartre. Dual Hyperquaternion Poincaré Groups. Advances in Applied Clifford Algebras, 2021, 31 (2), ⟨10.1007/s00006-021-01120-z⟩. ⟨hal-03139597⟩
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