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The inhomogeneous renormalization group equation for the effective potentialis rederived. It is shown that when the effective potential is normalized bythe normalization condition on the generating functional, its renormalizationgroup equation is homogeneous. This is demonstrated in the case of massive$\phi^4$-theory. We also show that for the case of spontaneous symmetrybreaking, the normalized effective potential is completely different from thesymmetric case, though the two cases satisfy the same RGE with the sameRG-functions. It is concluded that the vacuum energy density arises only in thecase of SSB.

Inhomogeneous and Homogeneous Renormalization Group Equations for the Effective Potential