 Vacuum polarization

Vacuum polarization is the modification of a gauge field's propagation by quantum fluctuations of charged fields. In quantum electrodynamics, charged-particle loop contributions change the photon propagator; their proper two-point insertion is photon vacuum polarization.

Lorentz invariance and the Ward identity constrain the tensor structure. For an invariant vacuum it is transverse and can be written ${\Pi }^{\mu \nu }(q)=(q^2{g}^{\mu \nu }-q^{\mu }{q}^{\nu })\Pi (q^2)$, up to the stated sign convention. This momentum-dependent response contributes to the scale dependence of the effective electromagnetic coupling. The calculation describes a field correlation, rather than a literal medium of separately detectable virtual pairs. A mass term for the photon is not generated merely by renormalizing a gauge-invariant vacuum polarization.