Rotationer, spinorer och spinn

Abstract

A central concept in quantum mechanics is spin. Certain quantum systems have the property that, at a full rotation, the system has not been reset, but is in the opposite configuration relative to the starting position. It is previously known that spin is hard to visualize. In this paper we have for this reason created a computer animation to show how spin arises and how it behaves. We have used the programming language MATLAB to do this. To be able to understand this animation it is necessary to have a basic understanding of spin. A central part of this paper will therefore consist of a review of the mathematical theory behind spin. We start by explaning the mathematical concepts of exterior algebra and Clifford algebra. Then we introduce quaternions and explain their connections to spin. Furthermore we explain the mathematical concepts of spinors and spinor space to describe spin. Finally we end the paper with explaining how the code is written and how it relates to spin.