QED Source Trick and Diagram Expansion

Generating functionals, source derivatives, and how perturbative diagrams emerge.

the qed path integral feynman diagrams perturbative qed

Exercise 1

Field insertions from functional derivatives

Advancedfunctional derivativesgenerating functionalqed

Suppose a scalar generating functional contains a source term $\int J\phi$ . Explain why a derivative with respect to $J(x)$ produces a field insertion at the point $x$ .

Subparts

Differentiate the source exponential formally once.

State what remains after setting $J=0$.

Exercise 2

Connected intuition for correlators

Intermediatecorrelatorsdiagrammaticsperturbation theory

Why is it advantageous to generate many correlators from one object rather than build each one directly from the path integral?

Subparts

Give one conceptual reason.

Give one practical reason relevant to perturbation theory.

Exercise 3

From expansion terms to diagrams

Advancedfeynman diagramswick contractionsqed

Explain in words how a perturbative expansion of the interaction exponential becomes a sum over Feynman diagrams.

Subparts

What does each power of the interaction term contribute?

How do contractions determine propagator lines?

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Sheet 3

QED Source Trick and Diagram Expansion

Generating functionals, source derivatives, and how perturbative diagrams emerge.

the qed path integral feynman diagrams perturbative qed

Exercise 1

Field insertions from functional derivatives

Advancedfunctional derivativesgenerating functionalqed

Suppose a scalar generating functional contains a source term $\int J\phi$ . Explain why a derivative with respect to $J(x)$ produces a field insertion at the point $x$ .