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A QFT question: you start from the lagrangian, compute the hamiltonian via Legendre transform and promote the the fields to operators with canonical equal-time commutation relations. Now you can compute the relation

[tex][H,F(x)]=-\mathrm{i}\partial_0 F(x) \ , [/tex]

where [tex]H[/tex] is the hamiltonian and [tex]F(x)[/tex] is a polynomial of the fields and/or their conjugate momenta. This implies that the hamiltonian is the generator of time translations. Does this mean that the QFT formalism automatically implies the validity of abstract Schrödinger's equation which states the same?

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# Abstract Schrödinger's equation in QFT

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