Is V_{eff} truly the density of effective action in QFT?

[ndung200790]

Please teach me this:
Why do we not call V_{eff}=\Gamma_{eff}/VT (where \Gamma_{eff} is the effective action, VT is spacetime volume) being density of effective action of field?
Thank you very much in advance.

 

[ndung200790]

I have just known(from Schoeder's QFT book) that V_{eff}=v_{0}(\Phi_{cl})\Phi^{4}_{cl}.Then this must be called effective potential,because it relates with interaction Phi-4(this case is an example) but must not be called density of action.Is that correct?