The current density in quantum electrodynamics in external potentials

Understand

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.