Lagrangian of self-dual gauge fields in various formulations

The Lagrangians of self-dual gauge theory in various formulations are reviewed. From these results we see a simple rule and use it to present some new non-covariant Lagrangian based on the decomposition of spacetime into D=D ₁+D ₂+D ₃. Our prescription could be easily extended to more complex decomposition of spacetime and some more examples are presented therefore. The self-dual property of the new Lagrangian is proved in detail. We also show that the new non-covariant actions give field equations with 6d Lorentz invariance.