On a Connection of the Fine Structure Constant with Zero-Point Fluctuations of the Electromagnetic Field in Vacuum*

Abstract

Duality of four-dimensional electrodynamics and two-dimensional field theory leads to a finite value $$ {e}_0=\pm \sqrt{\hbar c} $$ of the point-like bare charge with the fine structure constant a 0 = 1/4π. On the other hand, the calculated (by several authors) energy shifts E B = a B ћc/2r and E L = a L ћc/a of zero-point electromagnetic vacuum fluctuations by neutral conducting shells of a sphere of radius r and a cube of edge a are defined by the dimensionless parameters αB and αL, which differ from each other by less than 0.8% and even more weakly differ from the fine structure constant α times 4π, since a L < 4πa < a B. According to the duality, 4πα = α/α0 and α0αL < α < α0αB, the values αB and αL can be considered approximate reciprocals of the vacuum dielectric permittivity. Since the difference of α0αL from α appears to be less than 0.05%, we discuss here the possibility of circumscribing the sphere polyhedrons γ, the conducting shells of which could shift the zero-point energy by the amount Eγ = αγ_c/2r, where the parameter αγ is more close to 4πα than αL for the cube. We focus on the relativistic and adiabatic invariances of the parameters αγ.