{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/35685"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/35685","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"The relevance of the Pauli group in dynamical systems with pseudo-fermions","abstract":"The group of Wolfgang Pauli is well known in mathematical physics, because it describes some relevant symmetries in quantum dynamical systems. It is less known its structure of finite 2-group of order 16, which may be decomposed in the central product of two of its subgroups. From this perspective, the Pauli group has an interesting structure at an algebraic level as well. Here a topological perspective is added to the literature. It is described the Pauli group as an appropriate quotient of the fundamental group of 3-dimensional Riemannian surfaces constructed as two distinct orbit spaces of the 3-dimensional sphere S3 ; one orbit space comes from the free action of the quaternion group Q8 on S3 ; another orbit space comes from a similar action of the cyclic group Z(4) of order 4 on S3. Applications are illustrated for Pseudo-fermionic operators, introducing a relevant framework of quantum mechanics. This suggests a physical interpretation for the topological decomposition, which has been found at an abstract level.","abstract_html":"The group of Wolfgang Pauli is well known in mathematical physics, because it describes some relevant symmetries in quantum dynamical systems. It is less known its structure of finite 2-group of order 16, which may be decomposed in the central product of two of its subgroups. From this perspective, the Pauli group has an interesting structure at an algebraic level as well. Here a topological perspective is added to the literature. It is described the Pauli group as an appropriate quotient of the fundamental group of 3-dimensional Riemannian surfaces constructed as two distinct orbit spaces of the 3-dimensional sphere S3 ; one orbit space comes from the free action of the quaternion group Q8 on S3 ; another orbit space comes from a similar action of the cyclic group Z(4) of order 4 on S3. Applications are illustrated for Pseudo-fermionic operators, introducing a relevant framework of quantum mechanics. This suggests a physical interpretation for the topological decomposition, which has been found at an abstract level.","abstract_has_math":false,"creators":["Bavuma, Yanga"],"institution":"Department of Mathematics and Applied Mathematics","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Russo, Francesco"],"committee_chairs":[],"committee_members":[],"year":2021,"date_issued":"2021","date_published":"2021","updated_at":"2026-07-22T22:22:51Z","subjects":["Mathematics and Applied Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11427/35685","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Russo, Francesco"]},{"key":"dc:creator","label":"Author","values":["Bavuma, Yanga"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2022-02-09T11:29:26Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2022-02-09T11:29:26Z"]},{"key":"dc:date.issued","label":"Date","values":["2021"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Department of Mathematics and Applied Mathematics"]},{"key":"dc:type","label":"Dc Type","values":["Doctoral Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Doctoral","PhD"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics and Applied Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/11427/35685"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The group of Wolfgang Pauli is well known in mathematical physics, because it describes some relevant symmetries in quantum dynamical systems. It is less known its structure of finite 2-group of order 16, which may be decomposed in the central product of two of its subgroups. From this perspective, the Pauli group has an interesting structure at an algebraic level as well. Here a topological perspective is added to the literature. It is described the Pauli group as an appropriate quotient of the fundamental group of 3-dimensional Riemannian surfaces constructed as two distinct orbit spaces of the 3-dimensional sphere S3 ; one orbit space comes from the free action of the quaternion group Q8 on S3 ; another orbit space comes from a similar action of the cyclic group Z(4) of order 4 on S3. Applications are illustrated for Pseudo-fermionic operators, introducing a relevant framework of quantum mechanics. This suggests a physical interpretation for the topological decomposition, which has been found at an abstract level."]},{"key":"dc:title","label":"Title","values":["The relevance of the Pauli group in dynamical systems with pseudo-fermions"]}]}],"canonical_facts":{"dc:contributor.advisor":["Russo, Francesco"],"dc:creator":["Bavuma, Yanga"],"dc:date.accessioned":["2022-02-09T11:29:26Z"],"dc:date.available":["2022-02-09T11:29:26Z"],"dc:date.issued":["2021"],"dc:description.abstract":["The group of Wolfgang Pauli is well known in mathematical physics, because it describes some relevant symmetries in quantum dynamical systems. It is less known its structure of finite 2-group of order 16, which may be decomposed in the central product of two of its subgroups. From this perspective, the Pauli group has an interesting structure at an algebraic level as well. Here a topological perspective is added to the literature. It is described the Pauli group as an appropriate quotient of the fundamental group of 3-dimensional Riemannian surfaces constructed as two distinct orbit spaces of the 3-dimensional sphere S3 ; one orbit space comes from the free action of the quaternion group Q8 on S3 ; another orbit space comes from a similar action of the cyclic group Z(4) of order 4 on S3. Applications are illustrated for Pseudo-fermionic operators, introducing a relevant framework of quantum mechanics. This suggests a physical interpretation for the topological decomposition, which has been found at an abstract level."],"dc:identifier.uri":["http://hdl.handle.net/11427/35685"],"dc:publisher.department":["Department of Mathematics and Applied Mathematics"],"dc:subject":["Mathematics and Applied Mathematics"],"dc:title":["The relevance of the Pauli group in dynamical systems with pseudo-fermions"],"dc:type":["Doctoral Thesis"],"dc:type.qualificationlevel":["Doctoral","PhD"]},"updated_at":"2026-07-22T22:22:51Z"}