{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/17138"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/17138","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"Renormalization of cavity field theories","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Stoddart, A J"],"institution":"Department of Physics","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Viollier, Raoul D"],"committee_chairs":[],"committee_members":[],"year":1990,"date_issued":"1990","date_published":"1990","updated_at":"2026-07-24T01:33:45Z","subjects":[],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11427/17138","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Viollier, Raoul D"]},{"key":"dc:creator","label":"Author","values":["Stoddart, A J"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2016-02-18T12:24:46Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2016-02-18T12:24:46Z"]},{"key":"dc:date.issued","label":"Date","values":["1990"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Department of Physics"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Cape Town"]},{"key":"dc:type","label":"Dc Type","values":["Doctoral Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Doctoral"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["PhD"]}]},{"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/11427/17138"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Bibliography: pages 95-97."]},{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:title","label":"Title","values":["Renormalization of cavity field theories"]}]}],"canonical_facts":{"dc:contributor.advisor":["Viollier, Raoul D"],"dc:creator":["Stoddart, A J"],"dc:date.accessioned":["2016-02-18T12:24:46Z"],"dc:date.available":["2016-02-18T12:24:46Z"],"dc:date.issued":["1990"],"dc:description":["Bibliography: pages 95-97."],"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."],"dc:identifier.uri":["http://hdl.handle.net/11427/17138"],"dc:language.iso":["eng"],"dc:publisher.department":["Department of Physics"],"dc:publisher.institution":["University of Cape Town"],"dc:title":["Renormalization of cavity field theories"],"dc:type":["Doctoral Thesis"],"dc:type.qualificationlevel":["Doctoral"],"dc:type.qualificationname":["PhD"]},"updated_at":"2026-07-24T01:33:45Z"}