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Renormalization of cavity field theories
Bibliography: pages 95-97.
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| Format: | Thesis |
| Language: | English |
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Department of Physics
2016
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| _version_ | 1867613142723330048 |
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| access_status_str | Open Access |
| author | Stoddart, A J |
| author2 | Viollier, Raoul D |
| author_browse | Stoddart, A J Viollier, Raoul D |
| author_facet | Viollier, Raoul D Stoddart, A J |
| author_sort | Stoddart, A J |
| collection | Thesis |
| description | Bibliography: pages 95-97. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/17138 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:31:26.417Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2016 |
| publishDateRange | 2016 |
| publishDateSort | 2016 |
| publisher | Department of Physics |
| publisherStr | Department of Physics |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/17138 Renormalization of cavity field theories Stoddart, A J Viollier, Raoul D Physics Field theory (Physics) Bibliography: pages 95-97. A major obstacle to calculating Feynman diagrams in field theories, confined to a cavity, has always been the divergent loop diagrams. So far, only the quantum chromodynamic and electrodynamic self-energies of a ls1/2 quark, confined to a static spherical cavity, have been accurately calculated. These quantities are of immediate interest in the M.I.T. bag model. The existing methods to calculate loop diagrams are based on the multiple reflection scheme, in which the zero reflection term is separated out analytically, and evaluated separately. Thus far, there are some indications that this method is unsuitable for the quadratically divergent one loop vacuum polarization. In this thesis we firstly develop a set of Fourier transforms, appropriate to a discussion of renormalization in a cavity. Using these, we renormalize the cavity propagators to one loop for scalar, Dirac, and gauge fields. We then introduce a new computational method to subtract out the divergences, based on dimensional regularization. Using this method, we present results for various loop diagrams. The scalar φ⁴ theory is used as a pedagogical example. We then present the quark self-energy for several low lying cavity modes. Finally we tackle the long standing and hitherto unresolved question of the vacuum polarization. For this we give a detailed discussion of surface divergences, and present results for scalar quantum electrodynamics. We make a suggestion for the implementation of the running coupling constant in the cavity. 2016-02-18T12:24:46Z 2016-02-18T12:24:46Z 1990 Doctoral Thesis Doctoral PhD http://hdl.handle.net/11427/17138 eng application/pdf Department of Physics Faculty of Science University of Cape Town |
| spellingShingle | Physics Field theory (Physics) Stoddart, A J Renormalization of cavity field theories |
| thesis_degree_str | Doctoral |
| title | Renormalization of cavity field theories |
| title_full | Renormalization of cavity field theories |
| title_fullStr | Renormalization of cavity field theories |
| title_full_unstemmed | Renormalization of cavity field theories |
| title_short | Renormalization of cavity field theories |
| title_sort | renormalization of cavity field theories |
| topic | Physics Field theory (Physics) |
| url | http://hdl.handle.net/11427/17138 |
| work_keys_str_mv | AT stoddartaj renormalizationofcavityfieldtheories |