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Renormalization of the vector current in QED

Collins, John C. and Manohar, Aneesh V. and Wise, Mark B. (2006) Renormalization of the vector current in QED. Physical Review D, 73 (10). Art. No. 105019. ISSN 2470-0010. doi:10.1103/PhysRevD.73.105019.

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It is commonly asserted that the electromagnetic current is conserved and therefore is not renormalized. Within QED we show (a) that this statement is false, (b) how to obtain the renormalization of the current to all orders of perturbation theory, and (c) how to correctly define an electron number operator. The current mixes with the four-divergence of the electromagnetic field-strength tensor. The true electron number operator is the integral of the time component of the electron number density, but only when the current differs from the [overline MS]-renormalized current by a definite finite renormalization. This happens in such a way that Gauss's law holds: the charge operator is the surface integral of the electric field at infinity. The theorem extends naturally to any gauge theory.

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Additional Information:©2006 The American Physical Society (Received 14 March 2006; published 31 May 2006) This work was supported in part by DOE Grants No. DE-FG02-90ER-40577, No. DE-FG03-97ER40546, and No. DE-FG03-92ER40701. We thank S. Adler, M. Neubert, J. Rabin, M. Srednicki, and M. Voloshin for comments on the first version of this paper.
Subject Keywords:quantum electrodynamics; perturbation theory; renormalisation; conservation laws
Issue or Number:10
Record Number:CaltechAUTHORS:COLprd06
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:3671
Deposited By: Archive Administrator
Deposited On:25 Jun 2006
Last Modified:08 Nov 2021 20:11

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