{"id":{"repo_id":"oregon","oai_identifier":"oai:scholarsbank.uoregon.edu:1794/31895"},"canonical_url":"https://search.dev.ndltd.org/etd/oregon/oai:scholarsbank.uoregon.edu:1794/31895","repository":{"repo_id":"oregon","name":"University of Oregon","base_url":"https://scholarsbank.uoregon.edu/server/oai/request"},"display":{"title":"Atoms on a Worldline: A Path-Integral Approach to Electromagnetic Casimir Energies","abstract":"The Casimir effect arises from quantum fluctuations of the electromagnetic field and leads to observable forces between material bodies even in vacuum. While the Casimir force between simple geometries has been well studied, accurately calculating Casimir interactions in general or many-body configurations remains a challenging problem, especially when electromagnetic vector properties and material responses are taken into account. Among the primary advancements in computational tools for Casimir physics, the worldline path-integral approach provides a powerful alternative to traditional mode summation and scattering approaches by reformulating the quantum vacuum energy in terms of an ensemble of fluctuating particle paths. The worldline method offers strong potential for handling arbitrary geometries through intuitive Monte Carlo sampling and parallelizable algorithms. However, most prior worldline formulations are restricted to scalar fields or simplified boundary conditions. This dissertation aims to extend and strengthen the worldline formalism in both numerical and analytical directions. First, it develops a pathwise differentiation technique that enables efficient computation of Casimir forces and higher derivatives of the energy numerically. Second, the thesis contrasts with the Green-tensor formalism and investigates the breakdown of scalar approximations in electromagnetic Casimir worldlines between discrete polarizable atoms, highlighting the necessity of vectorial field treatments in the worldline method. These findings demonstrate the critical effects of electromagnetic polarization mixing in Casimir energy computations and suggest new pathways for studying dispersion forces in many-body systems.","abstract_html":"The Casimir effect arises from quantum fluctuations of the electromagnetic field and leads to observable forces between material bodies even in vacuum. While the Casimir force between simple geometries has been well studied, accurately calculating Casimir interactions in general or many-body configurations remains a challenging problem, especially when electromagnetic vector properties and material responses are taken into account. Among the primary advancements in computational tools for Casimir physics, the worldline path-integral approach provides a powerful alternative to traditional mode summation and scattering approaches by reformulating the quantum vacuum energy in terms of an ensemble of fluctuating particle paths. The worldline method offers strong potential for handling arbitrary geometries through intuitive Monte Carlo sampling and parallelizable algorithms. However, most prior worldline formulations are restricted to scalar fields or simplified boundary conditions. This dissertation aims to extend and strengthen the worldline formalism in both numerical and analytical directions. First, it develops a pathwise differentiation technique that enables efficient computation of Casimir forces and higher derivatives of the energy numerically. Second, the thesis contrasts with the Green-tensor formalism and investigates the breakdown of scalar approximations in electromagnetic Casimir worldlines between discrete polarizable atoms, highlighting the necessity of vectorial field treatments in the worldline method. These findings demonstrate the critical effects of electromagnetic polarization mixing in Casimir energy computations and suggest new pathways for studying dispersion forces in many-body systems.","abstract_has_math":false,"creators":["Zheng, He"],"institution":"University of Oregon","degree_name":"Ph.D.","degree_level":"doctoral","degree_discipline":"Department of Physics","degree_department":null,"school":null,"contributors":[],"advisors":["Steck, Daniel"],"committee_chairs":[],"committee_members":[],"year":2025,"date_issued":"2025-11-19","date_published":"2025-11-19","updated_at":"2026-08-21T16:47:18Z","subjects":[],"languages":["en_US"],"rights":["All Rights Reserved."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/1794/31895","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"source_record":{"url":"https://scholarsbank.uoregon.edu/server/oai/request?verb=GetRecord&metadataPrefix=dim&identifier=oai%3Ascholarsbank.uoregon.edu%3A1794%2F31895","prefix":"dim"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Steck, Daniel"]},{"key":"dc:creator","label":"Author","values":["Zheng, He"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2025-11-19T19:11:40Z"]},{"key":"dc:date.issued","label":"Date","values":["2025-11-19"]},{"key":"dc:publisher","label":"Institution","values":["University of Oregon"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation or thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Department of Physics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Oregon"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en_US"]},{"key":"dc:rights","label":"Dc Rights","values":["All Rights Reserved."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/1794/31895"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The Casimir effect arises from quantum fluctuations of the electromagnetic field and leads to observable forces between material bodies even in vacuum. While the Casimir force between simple geometries has been well studied, accurately calculating Casimir interactions in general or many-body configurations remains a challenging problem, especially when electromagnetic vector properties and material responses are taken into account. Among the primary advancements in computational tools for Casimir physics, the worldline path-integral approach provides a powerful alternative to traditional mode summation and scattering approaches by reformulating the quantum vacuum energy in terms of an ensemble of fluctuating particle paths. The worldline method offers strong potential for handling arbitrary geometries through intuitive Monte Carlo sampling and parallelizable algorithms. However, most prior worldline formulations are restricted to scalar fields or simplified boundary conditions. This dissertation aims to extend and strengthen the worldline formalism in both numerical and analytical directions. First, it develops a pathwise differentiation technique that enables efficient computation of Casimir forces and higher derivatives of the energy numerically. Second, the thesis contrasts with the Green-tensor formalism and investigates the breakdown of scalar approximations in electromagnetic Casimir worldlines between discrete polarizable atoms, highlighting the necessity of vectorial field treatments in the worldline method. These findings demonstrate the critical effects of electromagnetic polarization mixing in Casimir energy computations and suggest new pathways for studying dispersion forces in many-body systems."]},{"key":"dc:title","label":"Title","values":["Atoms on a Worldline: A Path-Integral Approach to Electromagnetic Casimir Energies"]}]}],"canonical_facts":{"dc:contributor.advisor":["Steck, Daniel"],"dc:creator":["Zheng, He"],"dc:date.accessioned":["2025-11-19T19:11:40Z"],"dc:date.issued":["2025-11-19"],"dc:description.abstract":["The Casimir effect arises from quantum fluctuations of the electromagnetic field and leads to observable forces between material bodies even in vacuum. While the Casimir force between simple geometries has been well studied, accurately calculating Casimir interactions in general or many-body configurations remains a challenging problem, especially when electromagnetic vector properties and material responses are taken into account. Among the primary advancements in computational tools for Casimir physics, the worldline path-integral approach provides a powerful alternative to traditional mode summation and scattering approaches by reformulating the quantum vacuum energy in terms of an ensemble of fluctuating particle paths. The worldline method offers strong potential for handling arbitrary geometries through intuitive Monte Carlo sampling and parallelizable algorithms. However, most prior worldline formulations are restricted to scalar fields or simplified boundary conditions. This dissertation aims to extend and strengthen the worldline formalism in both numerical and analytical directions. First, it develops a pathwise differentiation technique that enables efficient computation of Casimir forces and higher derivatives of the energy numerically. Second, the thesis contrasts with the Green-tensor formalism and investigates the breakdown of scalar approximations in electromagnetic Casimir worldlines between discrete polarizable atoms, highlighting the necessity of vectorial field treatments in the worldline method. These findings demonstrate the critical effects of electromagnetic polarization mixing in Casimir energy computations and suggest new pathways for studying dispersion forces in many-body systems."],"dc:identifier.uri":["https://hdl.handle.net/1794/31895"],"dc:language.iso":["en_US"],"dc:publisher":["University of Oregon"],"dc:rights":["All Rights Reserved."],"dc:title":["Atoms on a Worldline: A Path-Integral Approach to Electromagnetic Casimir Energies"],"dc:type":["Dissertation or thesis"],"thesis:degree_discipline":["Department of Physics"],"thesis:degree_level":["doctoral"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Oregon"]},"updated_at":"2026-08-21T16:47:18Z"}