Bhupendra C. S. Chauhan and P. S. Bisht and O. P. S. Negi Octonionic Reformulation of Vector Analysis
310 - 314
2011
5
3
International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering http://waset.org/publications/10819
http://waset.org/publications/51
World Academy of Science, Engineering and Technology
According to celebrated Hurwitz theorem, there exists
four division algebras consisting of R (real numbers), C (complex
numbers), H (quaternions) and O (octonions). Keeping in view
the utility of octonion variable we have tried to extend the three
dimensional vector analysis to seven dimensional one. Starting with
the scalar and vector product in seven dimensions, we have redefined
the gradient, divergence and curl in seven dimension. It is shown
that the identity n(n 1)(n 3)(n 7) 0 is satisfied only
for 0, 1, 3 and 7 dimensional vectors. We have tried to write all
the vector inequalities and formulas in terms of seven dimensions
and it is shown that same formulas loose their meaning in seven
dimensions due to nonassociativity of octonions. The vector formulas
are retained only if we put certain restrictions on octonions and split
octonions.
International Science Index 51, 2011