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The symplectic analysis of a four dimensional $BF$ theory in the context ofthe Faddeev-Jackiw symplectic approach is performed. It is shown that thismethod is more economical than Dirac's formalism. In particular, the completeset of Faddeev-Jackiw constraints and the generalized Faddeev-Jackiw bracketsare reported. In addition, we show that the generalized Faddeev-Jackiw bracketsand the Dirac ones coincide to each other. Finally, the similarities andadvantages between Faddeev-Jackiw method and Dirac's formalism are brieflydiscussed.

Faddeev-Jackiw quantization of four dimensional BF theory