  We propose a framework for Lorentz-invariant Lagrangian field theories where
Ostrogradsky's scalar ghosts could be absent. A key ingredient is the
generalized Kronecker delta. The general Lagrangians are reformulated in the
language of differential forms. The absence of higher order equations of motion
for the scalar modes stems from the basic fact that every exact form is closed.
The well-established Lagrangian theories for spin-0, spin-1, p-form, spin-2
fields have natural formulations in this framework. We also propose novel
building blocks for Lagrangian field theories. Some of them are novel nonlinear
derivative terms for spin-2 fields. It is nontrivial that Ostrogradsky's scalar
ghosts are absent in these fully nonlinear theories.
