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?