On the Geometry of the Hyperbolic Scator Space in 1+2 Dimensions
We consider the scator space in 1+2 dimensions—a hypercomplex, non-distributive hyperbolic algebra introduced by Fernández-Guasti and Zaldívar. We find a method for treating scators algebraically by embedding them into a distributive and commutative algebra. A notion of dual scators is introduced an...
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| Veröffentlicht in: | Advances in applied Clifford algebras 2017-06, Vol.27 (2), p.1369-1386 |
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| container_title | Advances in applied Clifford algebras |
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| creator | Kobus, Artur Cieśliński, Jan L. |
| description | We consider the scator space in 1+2 dimensions—a hypercomplex, non-distributive hyperbolic algebra introduced by Fernández-Guasti and Zaldívar. We find a method for treating scators algebraically by embedding them into a distributive and commutative algebra. A notion of dual scators is introduced and discussed. We also study isometries of the scator space. It turns out that zero divisors cannot be avoided while dealing with these isometries. The scator algebra may be endowed with a nice physical interpretation, although it suffers from lack of some physically demanded important features. Despite that, there arise some open questions, e.g., whether hypothetical tachyons can be considered as usual particles possessing time-like trajectories. |
| doi_str_mv | 10.1007/s00006-016-0658-x |
| format | Article |
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| subjects | Algebra Applications of Mathematics Mathematical and Computational Physics Mathematical Methods in Physics Physics Physics and Astronomy Tachyons Theoretical |
| title | On the Geometry of the Hyperbolic Scator Space in 1+2 Dimensions |
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