On the WKB quantum equivalence between diverse p-brane actions

We consider an action for a closed, bosonic, p-brane, where the brane tension is not an assigned parameter but rather it is induced by a maximal rank gauge p-form. This model is classically equivalent to the Nambu–Goto/Howe-Tucker model. We investigate how this classical equivalence can be implemented in the path integral framework. For this purpose we adopt a first order'' integration procedure over gauge p-forms and a shortened’’ Fadeev-Popov procedure.