  We demonstrate that the four (3 + 1)-dimensional free Abelian 2-form gauge
theory presents a tractable field theoretical model for the Hodge theory where
the well-defined symmetry transformations correspond to the de Rham
cohomological operators of differential geometry. The conserved charges,
corresponding to the above continuous symmetry transformations, obey an algebra
that is reminiscent of the algebra obeyed by the cohomological operators. The
discrete symmetry transformation of the theory represents the realization of
the Hodge duality operation that exists in the relationship between the
exterior and co-exterior derivatives of differential geometry. Thus, we provide
the realizations of all the mathematical quantities, associated with the de
Rham cohomological operators, in the language of the symmetries of the present
4D free Abelian 2-form gauge theory.
