The Physical applications of complex and dual quaternions

ABSTRACT PhD Thesis THE PHYSICAL APPLICATIONS OF COMPLEX AND DUAL QUATERNIONS SÜLEYMAN DEMH* Anadolu University Graduate School of Natural and Applied Sciences Physics Program Supervisor: Prof. Dr. Kudret OZDAŞ 2003, 130 pages In this thesis, general definitions of real, complex and dual quaternions and their possible applications in physics were investigated. Since quaternions with four parameters include the 3-dimensional vector space, the physical quantities related to vectors were shown to be vector quaternions. Some of these expressions in quaternion space were given. After demonstrating the isomorphic matrix representations of complex and dual quaternions, Lorentz transformations, Maxwell's equations, classical and relativistic equations related to electromagnetism were derived in compact and expanded forms, respectively, both for quaternions and matrix representations. It was shown that the complex and dual quaternionic theory of generalized electromagnetic fields enhances the dimensionality of these representations from the 4-dimensional to the 8-dimensional vector space. Keywords: Quaternions, Electromagnetism, Maxwell's equations, Relativistic mechanics n