The current density in quantum electrodynamics in external potentials

Abstract

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.

24 pages, 1 figure; v2: final version

References in corpus (15)

• The Chiral Magnetic Effect
• The generally covariant locality principle -- A new paradigm for local quantum physics
• Local Wick Polynomials and Time Ordered Products of Quantum Fields in Curved Spacetime
• Quantum fields in curved spacetime
• Conservation of the stress tensor in perturbative interacting quantum field theory in curved spacetimes
• The Necessity of the Hadamard Condition
• Stable cosmological models driven by a free quantum scalar field
• A spin-statistics theorem for quantum fields on curved spacetime manifolds in a generally covariant framework
• A smooth introduction to the wavefront set
• The Casimir Effect for Fermions in One Dimension
• The locally covariant Dirac field
• Quantum Energy Inequalities and local covariance I: Globally hyperbolic spacetimes
• A General PCT Theorem for the Operator Product Expansion in Curved Spacetime
• The renormalized locally covariant Dirac field
• Locally covariant chiral fermions and anomalies

Cited by in corpus (7)

• The renormalized charged scalar current in the Reissner-Nordström-de Sitter spacetime
• The semiclassical energy density of kinks and solitons
• The semi-classical energy of open Nambu-Goto strings
• The current density in quantum electrodynamics in time-dependent external potentials and the Schwinger effect
• Vacuum polarization near boundaries
• Weather Forecast for Vacuum Fluctuations in QED
• Møller maps for Dirac fields in external backgrounds