Casimir Energy For Perfect Electric Conductors Using the A-Phi Formulation

Previous work by Reid, et.al. [1] calculated the Casimir energy for conducting geometries using the method of moments applied to the impedance matrix given by Electric Field Integral Equation (EFIE). His results were later extended by Atkins [2] by making use of the Argument Principle applied to the EFIE and transforming the calculation of the Casimir energy to one that used the Augmented EFIE (AEFIE) as its impedance matrix. We will use the same approach as Atkins but instead of using the AEFIE, we will propose using the A-Phi [3] formulation impedance matrix in order to calculate the Casimir energy for 2-D conducting geometries.

[1] M. T. Reid, A. W. Rodriguez, Jacob White, Steven G. Johnson. PRL 103. 040401. (2009).
[2] Phillip R. Atkins, Qi I. Dai, Wei E. I. Sha, Weng C. Chew. "CASIMIR FORCE FOR ARBITRARY OBJECTS USING THE ARGUMENT PRINCIPLE AND BOUNDARY ELEMENT METHODS". Progress in Electromagnetics Research. Vol 142. 615-624. (2013).
[3] Qin S. Liu, Sheng Sun, Weng Cho Chew. "A Potential-Based Integral Equation Method for Low-Frequency Electromagnetic Problems". IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 66, NO. 3, MARCH 2018.