Star products and geometric algebra [Elektronische Ressource] / vorgelegt von Peter Henselder

Star Products and Geometric AlgebraDissertationzur Erlangung des akademischen Grades einesDoctor rerum naturaliumvorgelegt vonDipl.-Phys. Peter HenselderUniversit¨at DortmundSeptember 2007For my parentsThought and science are raising problems whichtheir terms of study can never answer, many ofwhich are doubtless problems only for thought. Thetrisection of an angle is similarly an insoluble prob-lemonlyforcompassandstraight-edgeconstruction,and Achilles cannot overtake the tortoise so longas their progress is considered piecemeal, endlesslyhalving the distance between them. However, asit is not Achilles but the method of measurementwhich fails to catch up with the tortoise, so it is notman but his method of thought which fails to findfulfillment in experience. This is by no means to saythat science and analytic thought are useless anddestructive tools, but rather that the people whouse them must be greater than their tools. To be aneffective scientist one must be more than a scientist,and a philosopher must be more than a thinker. Forthe analytic measurement of nature tells us nothingif we cannot see nature in any other way.Alan W. WattsContentsIntroduction 21 The Star Product Formalism 41.1 Quantization and its Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2 Star Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.