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Entropic corrections to Coulomb’s law. (English) Zbl 1248.81137

Summary: Two well-known quantum corrections to the area law have been introduced in the literatures, namely, logarithmic and power-law corrections. Logarithmic corrections, arises from loop quantum gravity due to thermal equilibrium fluctuations and quantum fluctuations, while, power-law correction appears in dealing with the entanglement of quantum fields in and out the horizon. Inspired by Verlinde’s argument on the entropic force, and assuming the quantum corrected relation for the entropy, we propose the entropic origin for the Coulomb’s law in this note. Also we investigate the Uehling potential as a radiative correction to Coulomb potential in 1-loop order and show that for some value of distance the entropic corrections of the Coulomb’s law is compatible with the vacuum-polarization correction in QED. So, we derive modified Coulomb’s law as well as the entropy corrected Poisson’s equation which governing the evolution of the scalar potential \(\phi \). Our study further supports the unification of gravity and electromagnetic interactions based on the holographic principle.

MSC:

81T20 Quantum field theory on curved space or space-time backgrounds
81V10 Electromagnetic interaction; quantum electrodynamics
83C45 Quantization of the gravitational field
94A17 Measures of information, entropy
81V17 Gravitational interaction in quantum theory
83F05 Relativistic cosmology
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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