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Vacuum Polarization

The modification of the electromagnetic field in the vacuum due to the constant creation and annihilation of virtual electron-positron pairs.
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The statement of the theorem

The vacuum polarization correction Π(q2)\Pi(q^2) modifies the photon propagator Dμν(q)D_{\mu\nu}(q) by adding a self-energy term: Dμν(q)=−igμνq2+−igμαq2Π(q2)−igανq2+O(Π2)D_{\mu\nu}(q) = \frac{-i g_{\mu\nu}}{q^2} + \frac{-i g_{\mu\alpha}}{q^2} \Pi(q^2) \frac{-i g_{\alpha\nu}}{q^2} + O(\Pi^2) The polarization tensor Π(q2)\Pi(q^2) is calculated from the electron-positron loop integral: Π(q2)=−e2∫d4k(2π)4Tr[γμSF(k+q)γνSF(k)]\Pi(q^2) = -e^2 \int \frac{d^4 k}{(2\pi)^4} \text{Tr} \left[ \gamma^{\mu} S_F(k+q) \gamma^{\nu} S_F(k) \right] where SF(k)=i(γ⋅k+m)k2−m2+iϵS_F(k) = \frac{i(\gamma \cdot k + m)}{k^2 - m^2 + i\epsilon} is the fermion propagator.
Source: Wikipedia