Application of electromagnetic theory on quaternion

ABSTRACT Master of Science Thesis APPLICATION OF ELECTROMAGNETIC THEORY ON QUATERNIONS NURAY CANDEMİR Anadolu University Graduate School of Natural and Applied Science Physics Program Supervisor: Prof. Dr. Kudret OZDAŞ 2001, 35 pages In this thesis, quaternion and complex quaternion which are a system of numbers as real and complex numbers are defined. The general properties of algebra which are composed of these number systems are given. Since quaternion and complex quaternion algebra are associated to each other their matrix representation are investigated. 2x2 Complex matrix representation and 4x4 reel matrix representation of quaternions, 2x2 and 4x4 complex matrix representation and 8x8 reel matrix representation of complex quaternion are given. Electromagnetic theory, specially Maxwell's equations that are considered as an abstract of electromagnetic theory, continuity equation that is expressed in terms of charge conservation, and Poynting theorem that gives energy conservation are discussed. Then, using quaternion and complex quaternion algebra the way of expressing Maxwell's equation, continuity equation and Poynting theorem are shown. As Maxwell's four equations could be expressed in two equations in terms of quaternion, and it was found that it could also be combined into a single equation in terms of complex quaternion. Keywords: Quaternion, Complex Quaternion, Electromagnetic Theory