A. Zee, Quantum Field Theory in a Nutshell · Problem III.8.3

Field Theory Redux

Physics — QFT

Problem

Prove (28). [Hint: Do unto ∫d4xeiqx⟨0∣[O(x),O(0)]∣0⟩\int d^4x e^{iqx}\langle 0| [O(x), O(0)]|0\rangle what we did to ∫d4xeiqx⟨0∣∣T(O(x)O(0))∣0⟩\int d^4x e^{iqx}\langle 0||T (O(x)O(0))|0\rangle, namely, insert 1=∑n∣n⟩⟨n∣1 = \sum_n |n\rangle\langle n| (with ∣n⟩|n\rangle a complete set of states) between O(x)O(x) and O(0)O(0) in the commutator. Now we don't have to bother with representing the step function.]

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