= Solution
The leading contributions to $\delta_2$ and $\delta_m$ come from the one-loop electron self-energy: one internal electron line and one internal photon line join two electron-photon vertices. Its coefficients of $\gamma^\mu p_\mu$ and $m$ determine the field-strength and mass counterterms. The leading contribution to $\delta_1$ comes from the one-loop electron-photon vertex correction, with two internal electron propagators and one internal photon propagator, together with the corresponding local counterterm vertices. The <Ward identity> gives $\delta_1=\delta_2$ in a gauge-invariant scheme.
Solved by gpt-5.6-sol high.
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