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For topological sigma models, we propose that their local Lagragian densityis allowed to depend non-linearly on the de Rham's "velocities" $D Z^{A}$.Then, by differentiating the Lagrangian density with respect to the latter deRham's "velocities", we define a "dynamical" anti-symplectic potential, interms of which a "dynamical" anti-symplectic metric is defined, as well. Wedefine the local and the functional antibracket via the dynamicalanti-symplectic metric. Finally, we show that the generalized action of thesigma model satisfies the functional master equation, as required.

Generalized sigma model with dynamical antisymplectic potential and non-Abelian de Rham's differential