{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/35262"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/35262","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Topological Objects and Confinement in Non-Abelian Lattice Gauge Theory","abstract":"We use lattice methods to study the connection between topological objects and the confining potential in SU(2) and SU(3) Yang-Mills theories. We use Monte Carlo techniques, generating and performing measurements on sample configurations of SU(2) and SU(3) gauge fields. We isolate topological objects, specifically Abelian monopoles and center vortices, in these configurations. We then measure the contribution to the string tension from these objects, and compare the results to “full” measurements made on the original configurations. In addition we investigate the effects of gauge ambiguities (Gribov effects) and cooling on these sets of measurements. For the case of SU(2) lattice gauge theory, our results from monopoles agree with full values but are somewhat lower when gauge ambiguities are taken into account. The situation is not stable under cooling. When we carry out analogous procedures on sample SU(3) lattice configurations, we find disagreement between full SU(3) values and those from topological objects, with our results from topological objects being lower than the full SU(3) values. This disagreement becomes more substantial after the effects of gauge ambiguities are taken into account. We conclude that present methods for identifying and extracting topological objects are inadequate for explaining confinement in the realistic case of an SU(3) gauge group.","abstract_html":"We use lattice methods to study the connection between topological objects and the confining potential in SU(2) and SU(3) Yang-Mills theories. We use Monte Carlo techniques, generating and performing measurements on sample configurations of SU(2) and SU(3) gauge fields. We isolate topological objects, specifically Abelian monopoles and center vortices, in these configurations. We then measure the contribution to the string tension from these objects, and compare the results to “full” measurements made on the original configurations. In addition we investigate the effects of gauge ambiguities (Gribov effects) and cooling on these sets of measurements. For the case of SU(2) lattice gauge theory, our results from monopoles agree with full values but are somewhat lower when gauge ambiguities are taken into account. The situation is not stable under cooling. When we carry out analogous procedures on sample SU(3) lattice configurations, we find disagreement between full SU(3) values and those from topological objects, with our results from topological objects being lower than the full SU(3) values. This disagreement becomes more substantial after the effects of gauge ambiguities are taken into account. We conclude that present methods for identifying and extracting topological objects are inadequate for explaining confinement in the realistic case of an SU(3) gauge group.","abstract_has_math":false,"creators":["Tucker, William Walden"],"institution":null,"degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Physics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012-11-27T22:28:45Z","date_published":"2012-11-27T22:28:45Z","updated_at":"2026-07-22T22:25:31Z","subjects":["Topological","abelian","Lattice Gauge","monopoles","yang-mills","monte carlo","asymbiotic","quenched approximations","quark","antiquark","quark-antiquark","wilson loop","nielson-olesen","homotopy","invariants","polyakov","dirac","superconductor","gribov effect","submanifold","magnetic currents","overrelaxation"],"languages":["en"],"rights":["2005 Tucker ©"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/35262","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Tucker, William Walden"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2012-11-27T22:28:45Z","10000-01-01","2005"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation / Thesis","text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Physics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Topological","abelian","Lattice Gauge","monopoles","yang-mills","monte carlo","asymbiotic","quenched approximations","quark","antiquark","quark-antiquark","wilson loop","nielson-olesen","homotopy","invariants","polyakov","dirac","superconductor","gribov effect","submanifold","magnetic currents","overrelaxation"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["2005 Tucker ©"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/35262"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["We use lattice methods to study the connection between topological objects and the confining potential in SU(2) and SU(3) Yang-Mills theories. We use Monte Carlo techniques, generating and performing measurements on sample configurations of SU(2) and SU(3) gauge fields. We isolate topological objects, specifically Abelian monopoles and center vortices, in these configurations. We then measure the contribution to the string tension from these objects, and compare the results to “full” measurements made on the original configurations. In addition we investigate the effects of gauge ambiguities (Gribov effects) and cooling on these sets of measurements. For the case of SU(2) lattice gauge theory, our results from monopoles agree with full values but are somewhat lower when gauge ambiguities are taken into account. The situation is not stable under cooling. When we carry out analogous procedures on sample SU(3) lattice configurations, we find disagreement between full SU(3) values and those from topological objects, with our results from topological objects being lower than the full SU(3) values. This disagreement becomes more substantial after the effects of gauge ambiguities are taken into account. We conclude that present methods for identifying and extracting topological objects are inadequate for explaining confinement in the realistic case of an SU(3) gauge group.","Submitted by Elias Lopez (erlopez2@illinois.edu) on 2012-11-27T22:28:44Z No. of bitstreams: 1 Tucker_William.pdf: 1741856 bytes, checksum: d9e0c254b48698c737adf08c16b1bec2 (MD5)","Made available in DSpace on 2012-11-27T22:28:45Z (GMT). No. of bitstreams: 1 Tucker_William.pdf: 1741856 bytes, checksum: d9e0c254b48698c737adf08c16b1bec2 (MD5) Previous issue date: 2005","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Elias Lopez (erlopez2@illinois.edu) on 2012-11-27T22:28:45Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:09:43-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: Author has not yet granted open access permission","Author has not yet granted open access permission","U of I Only"]},{"key":"dc:title","label":"Title","values":["Topological Objects and Confinement in Non-Abelian Lattice Gauge Theory"]}]}],"canonical_facts":{"dc:creator":["Tucker, William Walden"],"dc:date":["2012-11-27T22:28:45Z","10000-01-01","2005"],"dc:description":["We use lattice methods to study the connection between topological objects and the confining potential in SU(2) and SU(3) Yang-Mills theories. We use Monte Carlo techniques, generating and performing measurements on sample configurations of SU(2) and SU(3) gauge fields. We isolate topological objects, specifically Abelian monopoles and center vortices, in these configurations. We then measure the contribution to the string tension from these objects, and compare the results to “full” measurements made on the original configurations. In addition we investigate the effects of gauge ambiguities (Gribov effects) and cooling on these sets of measurements. For the case of SU(2) lattice gauge theory, our results from monopoles agree with full values but are somewhat lower when gauge ambiguities are taken into account. The situation is not stable under cooling. When we carry out analogous procedures on sample SU(3) lattice configurations, we find disagreement between full SU(3) values and those from topological objects, with our results from topological objects being lower than the full SU(3) values. This disagreement becomes more substantial after the effects of gauge ambiguities are taken into account. We conclude that present methods for identifying and extracting topological objects are inadequate for explaining confinement in the realistic case of an SU(3) gauge group.","Submitted by Elias Lopez (erlopez2@illinois.edu) on 2012-11-27T22:28:44Z No. of bitstreams: 1 Tucker_William.pdf: 1741856 bytes, checksum: d9e0c254b48698c737adf08c16b1bec2 (MD5)","Made available in DSpace on 2012-11-27T22:28:45Z (GMT). No. of bitstreams: 1 Tucker_William.pdf: 1741856 bytes, checksum: d9e0c254b48698c737adf08c16b1bec2 (MD5) Previous issue date: 2005","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Elias Lopez (erlopez2@illinois.edu) on 2012-11-27T22:28:45Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:09:43-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: Author has not yet granted open access permission","Author has not yet granted open access permission","U of I Only"],"dc:identifier":["http://hdl.handle.net/2142/35262"],"dc:language":["en"],"dc:rights":["2005 Tucker ©"],"dc:subject":["Topological","abelian","Lattice Gauge","monopoles","yang-mills","monte carlo","asymbiotic","quenched approximations","quark","antiquark","quark-antiquark","wilson loop","nielson-olesen","homotopy","invariants","polyakov","dirac","superconductor","gribov effect","submanifold","magnetic currents","overrelaxation"],"dc:title":["Topological Objects and Confinement in Non-Abelian Lattice Gauge Theory"],"dc:type":["Dissertation / Thesis","text"],"thesis:degree_discipline":["Physics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."]},"updated_at":"2026-07-22T22:25:31Z"}