= Quantum effective potential
{title2=$\Gamma[\varphi=\text{constant}]=\int d^dx\,V_{\rm eff}(\varphi)$}
The quantum effective potential is the derivative-free part of the <quantum effective action> evaluated on a spatially constant background. The displayed sign uses $\Gamma=-W+\int J\varphi$ for $Z=e^{iW}$ and the source term $+J\phi$; the opposite effective-action convention gives $-\int V_{\rm eff}$. Its derivatives give zero-momentum <one-particle-irreducible vertices>. The value depends on a <renormalization scheme> and scale; an arbitrary additive vacuum-energy constant may be fixed separately.
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