Browsing by Author "Kirchner, Ulrich"

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    Approaches to ensembles of universes
    (2003) Kirchner, Ulrich; Ellis, GFR
    This thesis consists of three parts - each of them focusing on different aspects relating to ensembles of universes and causally disconnected regions. In the first part I investigate possible measures over the space of FLRW models. In the second part I examine the behaviour of such transition regions for spherically symmetric space-times. In the last part of this thesis I discuss philosophical, physical, and probabilistic issues related to the concept of a multiverse - an ensemble of universes. The difference between ensembles of really existing universes and ensembles of possible universes is emphasized.
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    A space-time approach to quantum mechanics
    (1999) Kirchner, Ulrich; Ellis, GFR
    We present a systematic development and application of Geometric Algebra, an extended vector calculus. The entire algebraic structure, which is a graded Clifford algebra, is developed. To illustrate the derived results, examples are given for two and three dimensions. Here it becomes clear, how rotations and Lorentz boosts can be formulated in the Geometric Algebra. Further we realize that the Geometric Algebra contains elements, which can be used as representations of the complex unit. Having derived the necessary tools, we turn our attention to physics. We give applications to classical mechanics, quantum mechanics, ï¬ eld theory, curved manifolds, electromagnetism, and gravity as a gauge theory.