Srednicki — Quantum Field Theory · Problem 68.1

Canonical Quantization of Scalar Fields — Mark Srednicki

Physics — QFT · current-correlation-function-spinor-qed

Problem

Consider the current correlation function

\langle 0|\mathrm{T}j^\mu(x)j^\nu(y)|0\rangle

in spinor electrodynamics. a) Show that its Fourier transform is proportional to

\Pi^{\mu\nu}(k) + \Pi^{\mu\rho}(k)\tilde{\Delta}_{\rho\sigma}(k)\Pi^{\sigma\nu}(k) + \dots \tag{68.14}

b) Use this to prove that

\Pi^{\mu\nu}(k)

is transverse:

k_\mu \Pi^{\mu\nu}(k) = 0