Dual BRST symmetry for QED

We show the existence of a co(dual)-BRST symmetry for the usual BRST invariant Lagrangian density of an Abelian gauge theory in two dimensions of space-time where a U(1) gauge field is coupled to the Noether conserved current (constructed by the Dirac fields). Under this new symmetry, it is the gauge-fixing term that remains invariant and the symmetry transformations on the Dirac fields are analogous to the chiral transformations. This interacting theory is shown to provide a tractable field theoretical model for the Hodge theory. The Hodge dual operation is shown to correspond to a discrete symmetry in the theory and the extended BRST algebra for the generators of the underlying symmetries turns out to be reminiscent of the algebra obeyed by the de Rham cohomology operators of differential geometry.