88 research outputs found
Quaternions and Special Relativity
We reformulate Special Relativity by a quaternionic algebra on reals. Using
{\em real linear quaternions}, we show that previous difficulties, concerning
the appropriate transformations on the space-time, may be overcome. This
implies that a complexified quaternionic version of Special Relativity is a
choice and not a necessity.Comment: 17 pages, latex, no figure
Octonionic Representations of GL(8,R) and GL(4,C)
Octonionic algebra being nonassociative is difficult to manipulate. We
introduce left-right octonionic barred operators which enable us to reproduce
the associative GL(8,R) group. Extracting the basis of GL(4,C), we establish an
interesting connection between the structure of left-right octonionic barred
operators and generic 4x4 complex matrices. As an application we give an
octonionic representation of the 4-dimensional Clifford algebra.Comment: 14 pages, Revtex, J. Math. Phys. (submitted
- …