I heard that in classical field theory, terms in the Lagrangian cannot have more than two derivatives acting on them. Why is this?(adsbygoogle = window.adsbygoogle || []).push({});

In quantum field theory, I read somewhere that having more than two derivatives on a term in the Lagrangian leads to a violation of Poincare invariance. Is this true?

One thing I derived is that, for a scalar field, if you accept the canonical commutation relations as true:

[tex]

[\phi(x,t),\Pi(y,t)]=i\delta^3(x-y)

[/tex]

then unless your canonical momentum [tex]\Pi(x,t) [/tex] is equal to [tex]\dot{\phi}(x,t) [/tex], then the commutation relations of the Fourier components of [tex]\phi(x,t) [/tex] no longer obey equations like:

[tex]

[a(k,t),a^\dagger(q,t)]=\delta^3(k-q)

[/tex]

or using a different normalization scheme:

[tex]

[a(k,t),a^\dagger(q,t)]=\delta^3(k-q)(2\pi)^32E_k

[/tex]

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# 3rd order derivatives in the lagrangian

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