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Why the Lagrangian in QFT must involve derivative of field? Is it correct that because fermions and bosons(meaning all things) obey Dirac and Klein-Gordon equations,then the corresponding Lagrangians include the derivative of field?

(I know that the derivative has a important role in Gauge Local Symmetries(leading to comparator that reserve the Gauge Symmetry of the derivative))

Thank you very much for your kind helping.

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# Why the Lagrangian must involve derivative of field?

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