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Title: Vacuum polarization in Coulomb field revisited

Abstract

Simplified derivation of Wichmann–Kroll term is presented. The derivation uses two formulas for hypergeometric functions, but otherwise is elementary. It is found that Laplace transform of the vacuum charge density diverges at zero momentum transfer. This divergence has nothing to do with known ultraviolet divergence. The latter is related to the large momentum behavior of the pertinent integral, while the former to the small momentum behavior. When these divergences are removed, the energy shift caused by vacuum polarization for an ordinary hydrogen obtained here is in an exact agreement with the result obtained by Wichmann and Kroll. Also, for muonic hydrogen the result obtained here reasonably agrees with that given in literature.

Authors:
;
Publication Date:
OSTI Identifier:
22617492
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics; Journal Volume: 379; Other Information: Copyright (c) 2017 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BOUND STATE; CHARGE DENSITY; COULOMB FIELD; HYPERGEOMETRIC FUNCTIONS; LAPLACE TRANSFORMATION; MOMENTUM TRANSFER; QUANTUM ELECTRODYNAMICS; RENORMALIZATION; ULTRAVIOLET DIVERGENCES; VACUUM POLARIZATION

Citation Formats

Zamastil, J., E-mail: zamastil@karlov.mff.cuni.cz, and Šimsa, D. Vacuum polarization in Coulomb field revisited. United States: N. p., 2017. Web. doi:10.1016/J.AOP.2017.02.008.
Zamastil, J., E-mail: zamastil@karlov.mff.cuni.cz, & Šimsa, D. Vacuum polarization in Coulomb field revisited. United States. doi:10.1016/J.AOP.2017.02.008.
Zamastil, J., E-mail: zamastil@karlov.mff.cuni.cz, and Šimsa, D. Sat . "Vacuum polarization in Coulomb field revisited". United States. doi:10.1016/J.AOP.2017.02.008.
@article{osti_22617492,
title = {Vacuum polarization in Coulomb field revisited},
author = {Zamastil, J., E-mail: zamastil@karlov.mff.cuni.cz and Šimsa, D.},
abstractNote = {Simplified derivation of Wichmann–Kroll term is presented. The derivation uses two formulas for hypergeometric functions, but otherwise is elementary. It is found that Laplace transform of the vacuum charge density diverges at zero momentum transfer. This divergence has nothing to do with known ultraviolet divergence. The latter is related to the large momentum behavior of the pertinent integral, while the former to the small momentum behavior. When these divergences are removed, the energy shift caused by vacuum polarization for an ordinary hydrogen obtained here is in an exact agreement with the result obtained by Wichmann and Kroll. Also, for muonic hydrogen the result obtained here reasonably agrees with that given in literature.},
doi = {10.1016/J.AOP.2017.02.008},
journal = {Annals of Physics},
number = ,
volume = 379,
place = {United States},
year = {Sat Apr 15 00:00:00 EDT 2017},
month = {Sat Apr 15 00:00:00 EDT 2017}
}