Octonic representation of electromagnetic field equations
Abstract
In this paper we represent eightcomponent values "octons," generating associative noncommutative algebra. It is shown that the electromagnetic field in a vacuum can be described by a generalized octonic equation, which leads both to the wave equations for potentials and fields and to the system of Maxwell's equations. The octonic algebra allows one to perform compact combined calculations simultaneously with scalars, vectors, pseudoscalars, and pseudovectors. Examples of such calculations are demonstrated by deriving the relations for energy, momentum, and Lorentz invariants of the electromagnetic field.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 January 2009
 DOI:
 10.1063/1.3041499
 arXiv:
 arXiv:0802.2435
 Bibcode:
 2009JMP....50a2901M
 Keywords:

 03.50.De;
 02.10.Ud;
 41.20.q;
 Classical electromagnetism Maxwell equations;
 Linear algebra;
 Applied classical electromagnetism;
 Mathematical Physics
 EPrint:
 12 pages, 1 figure