Vacuum polarization tensor in inhomogeneous magnetic fields

Understand

We develop worldline numerical methods, which combine string-inspired with Monte-Carlo techniques, for the computation of the vacuum polarization tensor in inhomogeneous background fields for scalar QED.

• The algorithm satisfies the Ward identity exactly and operates on the level of renormalized quantities.
• We use the algorithm to study for the first time light propagation in a spatially varying magnetic field.
• Whereas a local derivative expansion applies to the limit of small variations compared to the Compton wavelength, the case of a strongly varying field can be approximated by a derivative expansion for the averaged field.