{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/14639"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/14639","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"A space-time approach to quantum mechanics","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Kirchner, Ulrich"],"institution":"Department of Mathematics and Applied Mathematics","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Ellis, GFR"],"committee_chairs":[],"committee_members":[],"year":1999,"date_issued":"1999","date_published":"1999","updated_at":"2026-07-22T22:23:26Z","subjects":[],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11427/14639","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Ellis, GFR"]},{"key":"dc:creator","label":"Author","values":["Kirchner, Ulrich"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2015-11-04T10:37:00Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2015-11-04T10:37:00Z"]},{"key":"dc:date.issued","label":"Date","values":["1999"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Department of Mathematics and Applied Mathematics"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Cape Town"]},{"key":"dc:type","label":"Dc Type","values":["Master Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Masters"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["MSc"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/11427/14639"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Includes bibliographical references."]},{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:title","label":"Title","values":["A space-time approach to quantum mechanics"]}]}],"canonical_facts":{"dc:contributor.advisor":["Ellis, GFR"],"dc:creator":["Kirchner, Ulrich"],"dc:date.accessioned":["2015-11-04T10:37:00Z"],"dc:date.available":["2015-11-04T10:37:00Z"],"dc:date.issued":["1999"],"dc:description":["Includes bibliographical references."],"dc:description.abstract":["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."],"dc:identifier.uri":["http://hdl.handle.net/11427/14639"],"dc:language.iso":["eng"],"dc:publisher.department":["Department of Mathematics and Applied Mathematics"],"dc:publisher.institution":["University of Cape Town"],"dc:title":["A space-time approach to quantum mechanics"],"dc:type":["Master Thesis"],"dc:type.qualificationlevel":["Masters"],"dc:type.qualificationname":["MSc"]},"updated_at":"2026-07-22T22:23:26Z"}