Geometric factors in the Bohr--Rosenfeld analysis of the measurability of the electromagnetic field

TL;DR

This paper calculates geometric factors in the Bohr-Rosenfeld analysis of electromagnetic field measurability using a Fourier-Bessel method, providing explicit series and closed-form expressions for spherical regions.

Contribution

It introduces a Fourier-Bessel approach to evaluate geometric factors in the Bohr-Rosenfeld analysis, enabling explicit series and closed-form solutions for spherical regions.

Findings

Fourier-Bessel series for geometric factors derived

Closed-form expressions obtained for spherical regions

Enhanced analytical tools for electromagnetic measurability analysis

Abstract

The Geometric factors in the field commutators and spring constants of the measurement devices in the famous analysis of the measurability of the electromagnetic field by Bohr and Rosenfeld are calculated using a Fourier--Bessel method for the evaluation of folding integrals, which enables one to obtain the general geometric factors as a Fourier--Bessel series. When the space region over which the factors are defined are spherical, the Fourier--Bessel series terms are given by elementary functions, and using the standard Fourier-integral method of calculating folding integrals, the geometric factors can be evaluated in terms of manageable closed-form expressions.