Renormalisation

2. Vacuum polarisation or photon self-energy

   • Lower order propagator $D_{\mu \nu }^0({\xi }_B)=\frac{-i}{p^2}(g_{\mu \nu }+({\xi }_B-1)\frac{p_{\mu }{p}_{\nu }}{p^2})$
   • Higher order corrections $=D_{\mu \nu }^0({\xi }_B)+D_{\mu \rho }^0(-i{\Pi }^{\rho \sigma })D_{\sigma \nu }^0({\xi }_B)+...$ to O(α), $-i{\Pi }^{\mu \nu }(p)=(-1)\int \frac{d^{D}k}{(2\pi {)}^D}\frac{Tr[]}{[k^2-m^2][(k+p{)}^2-m^2]}$
     • (while evaluating trace substitute delta(m2,p2) for denominator with x anol)

3. Vertex Correction

   • Tree Level ${\Gamma }_{\mu }^0=-i{e}_B{\gamma }_{\mu }$
   • Higher order corrections ${\Gamma }_{\mu }=-i{e}_B{\gamma }_{\mu }-i{e}_B{\Lambda }_{\mu }(p_1,p_2)+...$
   • At O(α)