On the WKB Quantum Equivalence between Diverse $p$-brane Actions

S. Ansoldi¹

Dipartimento di Fisica Teorica dell'Università,

Istituto Nazionale di Fisica Nucleare, Sezione di Trieste,

Strada Costiera 11, 34014-Trieste, Italy

C. Castro²

Center for Theoretical Studies of Physical Systems

Clark Atlanta University, Atlanta, GA30314

E.Spallucci³

Dipartimento di Fisica Teorica dell'Università,

Istituto Nazionale di Fisica Nucleare, Sezione di Trieste,

Strada Costiera 11, 34014-Trieste, Italy

Abstract:

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.