{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/7681"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/7681","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"Geometrical and nonperturbative aspects of low dimensional field theories","abstract":"We present a collection of results on solitons in low-dimensional classical field theory. We begin by reviewing the geometrical setting of he nonlinear ơ-model and demonstrate the integrability of the theory in two-dimensions on a symmetric target manifold. After reviewing the construction of soliton solutions in the 0(3) ơ-model we consider a class of gauged nonlinear ơ-models on two-dimensional axially-symmetric target spaces. We show that, for a certain choice of self-interaction, these models are all self-dual and analyze the resulting Bogomol'nyi equations in the BPS limit using techniques from dynamical systems theory. Our analysis is then extended to topologically massive gauge fields. We conclude with a deviation into exploring links between four-dimensional self-dual Yang-Mills equations and various lower-dimensional field theories. In particular, we show that at the level of equations of motion, the Euclidean Yang-Mills equations in light-cone coordinates reduce to the two-dimensional nonlinear ơ-model.","abstract_html":"We present a collection of results on solitons in low-dimensional classical field theory. We begin by reviewing the geometrical setting of he nonlinear ơ-model and demonstrate the integrability of the theory in two-dimensions on a symmetric target manifold. After reviewing the construction of soliton solutions in the 0(3) ơ-model we consider a class of gauged nonlinear ơ-models on two-dimensional axially-symmetric target spaces. We show that, for a certain choice of self-interaction, these models are all self-dual and analyze the resulting Bogomol'nyi equations in the BPS limit using techniques from dynamical systems theory. Our analysis is then extended to topologically massive gauge fields. We conclude with a deviation into exploring links between four-dimensional self-dual Yang-Mills equations and various lower-dimensional field theories. In particular, we show that at the level of equations of motion, the Euclidean Yang-Mills equations in light-cone coordinates reduce to the two-dimensional nonlinear ơ-model.","abstract_has_math":false,"creators":["Murugan, Jeffrey"],"institution":"Department of Mathematics and Applied Mathematics","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Barashenkov, Igor"],"committee_chairs":[],"committee_members":[],"year":2000,"date_issued":"2000","date_published":"2000","updated_at":"2026-07-22T22:22:51Z","subjects":[],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11427/7681","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Barashenkov, Igor"]},{"key":"dc:creator","label":"Author","values":["Murugan, Jeffrey"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-09-25T08:47:55Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-09-25T08:47:55Z"]},{"key":"dc:date.issued","label":"Date","values":["2000"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Department of Mathematics and Applied Mathematics"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Cape Town"]},{"key":"dc:type","label":"Dc Type","values":["Master Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Masters"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["MSc"]}]},{"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/11427/7681"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Bibliography: leaves 84-88"]},{"key":"dc:description.abstract","label":"Abstract","values":["We present a collection of results on solitons in low-dimensional classical field theory. We begin by reviewing the geometrical setting of he nonlinear ơ-model and demonstrate the integrability of the theory in two-dimensions on a symmetric target manifold. After reviewing the construction of soliton solutions in the 0(3) ơ-model we consider a class of gauged nonlinear ơ-models on two-dimensional axially-symmetric target spaces. We show that, for a certain choice of self-interaction, these models are all self-dual and analyze the resulting Bogomol'nyi equations in the BPS limit using techniques from dynamical systems theory. Our analysis is then extended to topologically massive gauge fields. We conclude with a deviation into exploring links between four-dimensional self-dual Yang-Mills equations and various lower-dimensional field theories. In particular, we show that at the level of equations of motion, the Euclidean Yang-Mills equations in light-cone coordinates reduce to the two-dimensional nonlinear ơ-model."]},{"key":"dc:title","label":"Title","values":["Geometrical and nonperturbative aspects of low dimensional field theories"]}]}],"canonical_facts":{"dc:contributor.advisor":["Barashenkov, Igor"],"dc:creator":["Murugan, Jeffrey"],"dc:date.accessioned":["2014-09-25T08:47:55Z"],"dc:date.available":["2014-09-25T08:47:55Z"],"dc:date.issued":["2000"],"dc:description":["Bibliography: leaves 84-88"],"dc:description.abstract":["We present a collection of results on solitons in low-dimensional classical field theory. We begin by reviewing the geometrical setting of he nonlinear ơ-model and demonstrate the integrability of the theory in two-dimensions on a symmetric target manifold. After reviewing the construction of soliton solutions in the 0(3) ơ-model we consider a class of gauged nonlinear ơ-models on two-dimensional axially-symmetric target spaces. We show that, for a certain choice of self-interaction, these models are all self-dual and analyze the resulting Bogomol'nyi equations in the BPS limit using techniques from dynamical systems theory. Our analysis is then extended to topologically massive gauge fields. We conclude with a deviation into exploring links between four-dimensional self-dual Yang-Mills equations and various lower-dimensional field theories. In particular, we show that at the level of equations of motion, the Euclidean Yang-Mills equations in light-cone coordinates reduce to the two-dimensional nonlinear ơ-model."],"dc:identifier.uri":["http://hdl.handle.net/11427/7681"],"dc:language.iso":["eng"],"dc:publisher.department":["Department of Mathematics and Applied Mathematics"],"dc:publisher.institution":["University of Cape Town"],"dc:title":["Geometrical and nonperturbative aspects of low dimensional field theories"],"dc:type":["Master Thesis"],"dc:type.qualificationlevel":["Masters"],"dc:type.qualificationname":["MSc"]},"updated_at":"2026-07-22T22:22:51Z"}