Unifying Theory for Casimir Forces: Bulk and Surface Formulations

Universe

Giuseppe Bimonte¹  Thorsten Emig² 

[1] Dipartimento di Fisica E. Pancini, Università di Napoli Federico II, Complesso Universitario di Monte S. An-gelo, Via Cintia, I-80126 Napoli, Italy;Laboratoire de Physique Théorique et Modèles Statistiques, CNRS UMR 8626, Université Paris-Saclay, 91405 Orsay CEDEX, France;

关键词: casimir forces;    fluctuation induced interactions;    stress tensor;    path integral;   

DOI  :  10.3390/universe7070225

来源: DOAJ

【 摘 要 】

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 the literature, their connection is often not entirely clear, and some of them have been introduced as purely numerical techniques. Here we present a unifying approach for the Casimir force and free energy that builds on both the Maxwell stress tensor and path integral quantization. The result is presented in terms of either bulk or surface operators that describe corresponding current fluctuations. Our surface approach yields a novel formula for the Casimir free energy. The path integral is presented both within a Lagrange and Hamiltonian formulation yielding different surface operators and expressions for the free energy that are equivalent. We compare our approaches to previously developed numerical methods and the scattering approach. The practical application of our methods is exemplified by the derivation of the Lifshitz formula.

【 授权许可】

Unknown