Faddeev-Jackiw Analysis of Topological Mass Generating Action

We analyze the gauge symmetry of a topological mass generating action in four dimensions which contains both a vector and a second rank antisymmetric tensor fields. In the Abelian case, this system induces an effective mass for the vector gauge field via a topological coupling $B \wedge F$ in the presence of a kinetic term for the antisymmetric tensor field $B$, while maintaining a gauge symmetry. On the other hand, for the non-Abelian case the $B$ field does not have a gauge symmetry unless an auxiliary vector field is introduced to the system. We analyze this change of symmetry in the Faddeev-Jackiw formalism, and show how the auxiliary vector field enhances the symmetry. At the same time this enhanced gauge symmetry becomes reducible. We also show this phenomenon in this analysis.