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The relevance of the Pauli group in dynamical systems with pseudo-fermions
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,...
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| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2022
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| _version_ | 1867613205376794624 |
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| access_status_str | Open Access |
| author | Bavuma, Yanga |
| author2 | Russo, Francesco |
| author_browse | Bavuma, Yanga Russo, Francesco |
| author_facet | Russo, Francesco Bavuma, Yanga |
| author_sort | Bavuma, Yanga |
| collection | Thesis |
| description | 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. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/35685 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:32:26.116Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2022 |
| publishDateRange | 2022 |
| publishDateSort | 2022 |
| publisher | Department of Mathematics and Applied Mathematics |
| publisherStr | Department of Mathematics and Applied Mathematics |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/35685 The relevance of the Pauli group in dynamical systems with pseudo-fermions Bavuma, Yanga Russo, Francesco Mathematics and Applied Mathematics 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. 2022-02-09T11:29:26Z 2022-02-09T11:29:26Z 2021 2022-02-08T08:25:11Z Doctoral Thesis Doctoral PhD http://hdl.handle.net/11427/35685 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science |
| spellingShingle | Mathematics and Applied Mathematics Bavuma, Yanga The relevance of the Pauli group in dynamical systems with pseudo-fermions |
| thesis_degree_str | Doctoral |
| title | The relevance of the Pauli group in dynamical systems with pseudo-fermions |
| title_full | The relevance of the Pauli group in dynamical systems with pseudo-fermions |
| title_fullStr | The relevance of the Pauli group in dynamical systems with pseudo-fermions |
| title_full_unstemmed | The relevance of the Pauli group in dynamical systems with pseudo-fermions |
| title_short | The relevance of the Pauli group in dynamical systems with pseudo-fermions |
| title_sort | relevance of the pauli group in dynamical systems with pseudo fermions |
| topic | Mathematics and Applied Mathematics |
| url | http://hdl.handle.net/11427/35685 |
| work_keys_str_mv | AT bavumayanga therelevanceofthepauligroupindynamicalsystemswithpseudofermions AT bavumayanga relevanceofthepauligroupindynamicalsystemswithpseudofermions |