Reconsidering the quantization of electrodynamics with boundary conditions and some measurable consequences

Abstract

We show that the commonly known conductor boundary conditions $E_{||}=B_\perp=0$ can be realized in two ways which we call 'thick' and 'thin' conductor. The 'thick' conductor is the commonly known approach and includes a Neumann condition on the normal component $E_\perp$ of the electric field whereas for a 'thin' conductor $E_\perp$ remains without boundary condition. Both types describe different physics already on the classical level where a 'thin' conductor allows for an interaction between the normal components of currents on both sides. On quantum level different forces between a conductor and a single electron or a neutral atom result. For instance, the Casimir-Polder force for a 'thin' conductor is by about 13% smaller than for a 'thick' one.