Renormalization of cavity field theories
| dc.contributor.advisor | Viollier, Raoul D | en_ZA |
| dc.contributor.author | Stoddart, A J | en_ZA |
| dc.date.accessioned | 2016-02-18T12:24:46Z | |
| dc.date.available | 2016-02-18T12:24:46Z | |
| dc.date.issued | 1990 | en_ZA |
| dc.description | Bibliography: pages 95-97. | en_ZA |
| dc.description.abstract | 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. | en_ZA |
| dc.identifier.apacitation | Stoddart, A. J. (1990). <i>Renormalization of cavity field theories</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Physics. Retrieved from http://hdl.handle.net/11427/17138 | en_ZA |
| dc.identifier.chicagocitation | Stoddart, A J. <i>"Renormalization of cavity field theories."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Physics, 1990. http://hdl.handle.net/11427/17138 | en_ZA |
| dc.identifier.citation | Stoddart, A. 1990. Renormalization of cavity field theories. University of Cape Town. | en_ZA |
| dc.identifier.ris | TY - Thesis / Dissertation AU - Stoddart, A J AB - 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. DA - 1990 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 1990 T1 - Renormalization of cavity field theories TI - Renormalization of cavity field theories UR - http://hdl.handle.net/11427/17138 ER - | en_ZA |
| dc.identifier.uri | http://hdl.handle.net/11427/17138 | |
| dc.identifier.vancouvercitation | Stoddart AJ. Renormalization of cavity field theories. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Physics, 1990 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/17138 | en_ZA |
| dc.language.iso | eng | en_ZA |
| dc.publisher.department | Department of Physics | en_ZA |
| dc.publisher.faculty | Faculty of Science | en_ZA |
| dc.publisher.institution | University of Cape Town | |
| dc.subject.other | Physics | en_ZA |
| dc.subject.other | Field theory (Physics) | en_ZA |
| dc.title | Renormalization of cavity field theories | en_ZA |
| dc.type | Doctoral Thesis | |
| dc.type.qualificationlevel | Doctoral | |
| dc.type.qualificationname | PhD | en_ZA |
| uct.type.filetype | Text | |
| uct.type.filetype | Image | |
| uct.type.publication | Research | en_ZA |
| uct.type.resource | Thesis | en_ZA |
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