Irreducible canonical approach to first-stage reducible second-class constraints. The example of gauge-fixed two- and one-forms with Stueckelberg coupling

The Dirac bracket for gauge-fixed two- and one-forms with Stueckelberg coupling is derived along an irreducible manner. The inferred results coincide with those from the reducible approach, hence our method puts on equal footing the irreducible and reducible second-class constraints.