Split quaternions and hyperbolic spinors

This thesis consists of six chapters. The first chapter is for preface. In the second chapter basic definitions and neccessary theorems at Minkowski space have been given. Also hyperbolic number system is intoroduced. In the third chapter, relations between the real quaternion and the indexed spinors were given as a new approach in the 3-dimensional Euclidean space. In the fourth section vector kinematics and split quaternion kinematics are introduced. The fifth section comprises the original part of thesis. This section is organized as two subsections. In the first subsection information about hyperbolic spinor is given. In the second subsection, the split quaternions and the hyperbolic spinors are derived from the vector formulation of the Euler's teorem. This theory is on the general displacement of a rigid body with a fixed point in the Minkowski space . Then, the relationship between the hyperbolic spinors and the split quaternions is given by this vector formulation. Moreover, a hyperbolic spinor formulation of rotations which is an extension of the split quaternions is obtained. In the sixth chapter the general evaluation of thesis and recommendations for new researches are given.