A. Zee, Quantum Field Theory in a Nutshell · Problem VIII.4.6

Field Theory Redux

Physics — QFT

Problem

For any polynomial W(Φ)W(\Phi) show that [W(Φ)]F=F[dW(ϕ)/dϕ]+[W(\Phi)]_F = F[dW(\phi)/d\phi] + terms not involving FF. Show that for the theory (11) the potential energy is given by V(ϕ†,ϕ)=∣∂W(ϕ)/∂ϕ∣2V(\phi^\dagger, \phi) = |\partial W(\phi)/\partial\phi|^2.

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