The one-loop correction to the laser-induced mass shift in QED is gauge dependent, vanishing in Landau gauge where only vacuum renormalisation is needed.
Polarization operator for plane-wave background fields
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abstract
We derive an alternative representation of the leading-order contribution to the polarization operator in strong-field quantum electrodynamics with a plane-wave electromagnetic background field, which is manifestly symmetric with respect to the external photon momenta. Our derivation is based on a direct evaluation of the corresponding Feynman diagram, using the Volkov representation of the dressed fermion propagator. Furthermore, the validity of the Ward-Takahashi identity is shown for general loop diagrams in an external plane-wave background field.
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One loop Volkov propagator in the Lorentz class of gauges
The one-loop correction to the laser-induced mass shift in QED is gauge dependent, vanishing in Landau gauge where only vacuum renormalisation is needed.