p-Branes as Composite Antisymmetric Tensor Field Theories

$p'$-brane solutions to rank $p+1$ composite antisymmetric tensor field theories of the kind developed by Guendelman, Nissimov and Pacheva are found when the dimensionality of spacetime is $D=(p+1)+(p'+1)$. These field theories posses an infinite dimensional group of global Noether symmetries, that of volume-preserving diffeomorphisms of the target space of the scalar primitive field constituents. Crucial in the construction of $p'$ brane solutions are the duality transformations of the fields and the local gauge field theory formulation of extended objects given by Aurilia, Spallucci and Smailagic. Field equations are rotated into Bianchi identities after the duality transformation is performed and the Clebsch potentials associated with the Hamilton-Jacobi formulation of the $p'$ brane can be identified with the $duals$ of the original scalar primitive constituents. Different types of Kalb-Ramond actions are discussed and a particular covariant action is presented which bears a direct relation to the light-cone gauge $p$-brane action. A simple derivation of $S$ and $T$ duality is also given. \medskip