Vacuum Polarization - Vacuum Polarization Tensor

Vacuum Polarization Tensor

The vacuum polarization is quantified by the vacuum polarization tensor Πμν(p) which describes the dielectric effect as a function of the four-momentum p carried by the photon. Thus the vacuum polarization depends on the momentum transfer, or in other words, the dielectric constant is scale dependent. In particular, for electromagnetism we can write the fine structure constant as an effective momentum-transfer-dependent quantity; to first order in the corrections, we have

where Πμν(p) = (p2 gμν - pμpν) Π(p2) and the subscript 2 denotes the leading order-e2 correction. The tensor structure of Πμν(p) is fixed by the Ward identity.