Electrostatics with a Finite-Range Nonlocal Polarization Kernel: Closed-Form Potential, Force-Law Deviations, Physical Motivation, and Experimental Context
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Description
We analyze a minimal, static, nonlocal modification of vacuum electrodynamics in which
the electric displacement D(r) depends on the electric field E(r) via an isotropic, finiterange
spatial susceptibility χ(|r − r′|). In electrostatics and for a point charge, the
modified Gauss law reduces in Fourier space to V (k) = ρ(k)/[k2(ε0 + χ(k))]. Choosing
χ(k) = χ0/(1 + k2ℓ2) produces a closed-form real-space potential with quadratic shortdistance
recovery and finite-range crossover. We demonstrate the effective field theory
origin through integrating out a gapped polarization mediator, derive the complete realspace
kernel, provide step-by-step algebraic derivations, and develop a dynamical extension
consistent with causality and passivity. We outline robust experimental observables for
AFM/MEMS precision force metrology and provide practical suggestions for dataset
reanalysis.
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References
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