Hyperquaternions and physics Article Swipe

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Patrick Girard , Romaric Pujol , Patrick Clarysse , Philippe Delachartre ·

YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.21468/scipostphysproc.14.030

The paper develops, within a new representation of Clifford algebras in terms of tensor products of quaternions called hyperquaternions, several applications. The first application is a quaternion 2D representation in contradistinction to the frequently used 3D one. The second one is a new representation of the conformal group in (1+2) space (signature +-- ) within the Dirac algebra C_{5}\left(2,3\right) \simeq \mathbb{C\otimes H\otimes H} subalgebra of \mathbb{H\otimes H\otimes H} . A numerical example and a canonical decomposition into simple planes are given. The third application is a classification of all hyperquaternion algebras into four types, providing the general formulas of the signatures and relating them to the symmetry groups of physics.

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Type: article
Language: en
Landing Page: https://doi.org/10.21468/scipostphysproc.14.030
PDF: https://scipost.org/10.21468/SciPostPhysProc.14.030/pdf
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DOI: https://doi.org/10.21468/scipostphysproc.14.030

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Title: Hyperquaternions and physics

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Publication year: 2023

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Publication date: 2023-11-24

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Authors: Patrick Girard, Romaric Pujol, Patrick Clarysse, Philippe Delachartre

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countries_distinct_count	1
institutions_distinct_count	4
citation_normalized_percentile.value	0.85311895
citation_normalized_percentile.is_in_top_1_percent	False
citation_normalized_percentile.is_in_top_10_percent	False