Unifying Theory for Casimir Forces: Bulk and Surface Formulations

The principles of the electromagnetic fluctuation-induced phenomena such as Casimir forces are well understood. However, recent experimental advances require universal and efficient methods to compute these forces. While several approaches have been proposed in literature, their connection is often not entirely clear, some them introduced purely numerical techniques. Here we present a unifying approach for force free energy that builds on both Maxwell stress tensor path integral quantization. result presented terms either bulk or surface operators describe corresponding current fluctuations. Our yields novel formula energy. within Lagrange Hamiltonian formulation yielding different expressions equivalent. We compare our previously developed scattering approach. practical application exemplified by derivation Lifshitz formula.