Electromagnetic energy conservation with complex octonions

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KANSU M. E., TANIŞLI M., DEMİR S.

TURKISH JOURNAL OF PHYSICS, vol.36, no.3, pp.438-445, 2012 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 36 Issue: 3
  • Publication Date: 2012
  • Doi Number: 10.3906/fiz-1109-18
  • Journal Name: TURKISH JOURNAL OF PHYSICS
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.438-445
  • Keywords: Octonion, Maxwell's equations, electromagnetic energy, Poynting vector
  • Anadolu University Affiliated: Yes

Abstract

Octonions are the eight dimensional hypercomplex numbers that form a noncommutative and non-associative division algebra. In this study, a general framework for the real, complex octonions and their algebra are provided by using the Cayley-Dickson multiplication rule between the octonionic basis elements. Maxwell's equations without sources are shown in Gauss units in dimensionless form. The local energy conservation equation, which has been previously defined in a complexified quaternionic form, is similarly rearranged for isotropic media by using the complex octonions. As a result, the terms of density and flow of electromagnetic energy are attained.