= Integration-by-parts reduction of scalar operators
{title2=$\phi^2(\partial\phi)^2\simeq-\phi^3\Box\phi/3$}
Two <Lagrangian densities> differing by a <total derivative> yield the same <action> under suitable <boundary conditions>. For example $\partial_\mu(\phi^3\partial^\mu\phi)=3\phi^2(\partial\phi)^2+\phi^3\Box\phi$. Likewise $\phi\Box^2\phi\simeq-\partial\phi\cdot\partial\Box\phi\simeq(\Box\phi)^2\simeq(\partial_\mu\partial_\nu\phi)^2$. These are algebraic relations modulo boundary terms, not uses of the <equation of motion>.
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