General Lagrangian of non-covariant self-dual gauge field

We present the general formulation of non-covariant Lagrangian of self-dual gauge theory. After specifying the parameters therein the previous Lagrangian in the decomposition of spacetime into 6 = D-1 + D-2 and 6 = D-1 + D-2 + D-3 can be obtained. The self-dual property of the general Lagrangian is proved in detail. We furthermore show that the new non-covariant actions give field equations with 6d Lorentz invariance. The method can be straightforwardly extended to any dimension and we also give a short discussion about the 10D self-dual gauge theory.