Srednicki — Quantum Field Theory · Problem 21.1

Canonical Quantization of Scalar Fields — Mark Srednicki

Physics — QFT · quantum-action-legendre-transform

Problem

Show that Γ(φ)=W(Jφ)−∫ddx Jφφ,(21.20)\Gamma(\varphi) = W(J_\varphi) - \int d^d x\, J_\varphi \varphi , \tag{21.20} where Jφ(x)J_\varphi(x) is the solution of δδJ(x)W(J)=φ(x)(21.21)\frac{\delta}{\delta J(x)} W(J) = \varphi(x) \tag{21.21} for a specified φ(x)\varphi(x).

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