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.
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Ritus, V.I. On a Connection of the Fine Structure Constant with Zero-Point Fluctuations of the Electromagnetic Field in Vacuum* . J Russ Laser Res 36, 101–109 (2015). https://doi.org/10.1007/s10946-015-9483-2
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DOI: https://doi.org/10.1007/s10946-015-9483-2