Octonionic representation of Maxwell equations and Dirac equation

iABSTRACTPhD ThesisOCTONIONIC REPRESENTATION OF MAXWELL EQUATIONS ANDDIRAC EQUATIONTülay TOLANAnadolu UniversityGraduate School of SciencesPhysics ProgramSupervisor: Prof. Kudret ÖZDAŞAssist. Prof. Dr. Murat TANIŞLI2006, 51 pagesIn this thesis; firstly the real, complex, and split octonion algebra, and theirmatrix representations are given. Next, the complex quaternions with equalcomponents are compared with octonions. Then, the differential operator, field,potential, and source octonions are defined, and for general octonionic fieldequation, potential equation and source independent fields which depend on theformer, the wave equation is written in octonion algebra. In these procedures,which are applications of octonion algebra to electromagnetic theory, both of theCayley-Dickson and the modul 7 methods given in the first part of the thesis areused for the product of basis elements. Lastly, as an application of octonionalgebra to quantum mechanics, Klein-Gordon and Dirac equations are shown inthe octonionic form.Keywords: Octonion Algebra, Field Equations, Maxwell Equations, Klein-Gordon Equation, Dirac Equation