Zur Nichtrelativistischen Näherung der Dirac-Gleichung im Gravitationsfeld der Erde

Abstract

The aim of this thesis is to collect and put into context the complete groundwork required for describing slow-moving uncharged fermions, like neutrons, above earth’s surface to obtain the general relativistic corrections that can be employed in experiments like qBOUNCE [4]. For this aim, we collect the necessary parts from a variety of already existing literature, work through them in detail, and arrange them such that they will be easy to use. In section 4 we shortly discuss how the bulk of the thesis might be used to calculate the relativistic corrections in question in subsequent investigations. In particular we will be establishing some background in general relativity, quantum mechanics, and 2-spinor formalism. We will then discuss, how these techniques could be used to describe a spin- 1 2 particle over the background of the Kerr-metric and to perform a Foldy-Wouthuysen transformation to obtain a Pauli equation with relativistic corrections. All this provides the necessary background for the search of hypothetical new interactions by using precision measurements.