Radiative Corrections and Renormalization in QED

Identify ultraviolet (UV) divergences in one-loop QED diagrams: electron self-energy, vacuum polarization, and vertex correction.

Apply dimensional regularization to isolate UV divergences in one-loop integrals.

Calculate the one-loop vacuum polarization tensor and renormalize the electric charge, leading to the concept of a running coupling constant.

Calculate the one-loop electron self-energy and renormalize the electron mass and field strength.

Calculate the one-loop vertex correction and relate it to the electron's anomalous magnetic moment (g-2).

Define the on-shell renormalization scheme and show how counterterms cancel the one-loop UV divergences in S-matrix elements.

Explain the physical significance of the running of the fine-structure constant α.

State the Ward-Takahashi identity and explain its role in guaranteeing the cancellation of divergences in QED.