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## Why no EOM in QFT with higher than second order derivatives in time and space?

When we write down a Lagragian for a quantum field theory, it is said that it should not depend on the second and higher order time and space derivatives of $$\phi$$, because we want the equation of motion(EOM) to be at most second order. Why is it so important. What trouble will a higher order EOM cuase in physics? Could anyone give me some examples? Thanks.

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