  We demonstrate that the celebrated St$\ddot u$ckelberg formalism gets
modified in the case of a massive four (3+1)-dimensional (4D) Abelian 2-form
theory due to the presence of a self-duality discrete symmetry in the theory.
The latter symmetry entails upon the modified 4D massive Abelian 2-form gauge
theory to become a massive model of Hodge theory within the framework of
Becchi-Rouet-Stora-Tyutin (BRST) formalism where there is existence of a set of
(anti-)co-BRST transformations corresponding to the usual nilpotent (anti-)BRST
transformations. The latter exist in any arbitrary dimension of spacetime for
the usual St$\ddot u$ckelberg-modified massive Abelian 2-form gauge theory. The
modification in the St$\ddot u$ckelberg technique is backed by the precise
mathematical arguments from the differential geometry where the exterior
derivative and Hodge duality operator play the decisive roles. The modified
version of the St$\ddot u$ckelberg technique remains invariant under the
discrete duality transformations which also establish a precise and deep
connection between the off-shell nilpotent (anti-)BRST and (anti-)co-BRST
transformations. We have clarified a simple trick to get rid of the higher
derivative terms in the appropriate Lagrangian densities so that our 4D theory
can become consistent and renormalizable.
