Atoms on a Worldline: A Path-Integral Approach to Electromagnetic Casimir Energies

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Department of Physics

Grantor dc:publisher

University of Oregon

Year dc:date.issued

2025

Author dc:creator

• Zheng, He

Advisor dc:contributor.advisor

• Steck, Daniel

Statement dc:rights

• All Rights Reserved.

Language dc:language.iso

en_US

Handle dc:identifier.uri

https://hdl.handle.net/1794/31895

OAI record oai:identifier

https://scholarsbank.uoregon.edu/server/oai/request?verb=GetRecord&metadataPrefix=dim&identifier=oai%3Ascholarsbank.uoregon.edu%3A1794%2F31895