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Title: The current density in quantum electrodynamics in external potentials

We review different definitions of the current density for quantized fermions in the presence of an external electromagnetic field. Several deficiencies in the popular prescription due to Schwinger and the mode sum formula for static external potentials are pointed out. We argue that Dirac’s method, which is the analog of the Hadamard point-splitting employed in quantum field theory in curved space–times, is conceptually the most satisfactory. As a concrete example, we discuss vacuum polarization and the stress–energy tensor for massless fermions in 1+1 dimension. Also a general formula for the vacuum polarization in static external potentials in 3+1 dimensions is derived.
Authors:
 [1] ;  [2]
  1. Fakultät für Physik, Universität Wien, Boltzmanngasse 5, 1090 Wien (Austria)
  2. Institut für Theoretische Physik, Universität Leipzig, Brüderstr. 16, 04103 Leipzig (Germany)
Publication Date:
OSTI Identifier:
22451194
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics; Journal Volume: 359; Other Information: Copyright (c) 2015 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:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CURRENT DENSITY; ELECTROMAGNETIC FIELDS; FERMIONS; QUANTUM ELECTRODYNAMICS; SPACE-TIME; TENSORS; VACUUM POLARIZATION