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Could you, please, elaborate? Where do the restrictions come from?
i think he just means that in QFT we (1) always impose lorentz invariance which heavily restricts the possible terms and (2) *usually* impose gauge symmetries on the lagrangian which further reduces the possible terms
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Yes indeed, including restrictions imposed by local gauge invariance and renormalization (e.g., powers of 5 or more of a scalar field are out).
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There are times when you have to relax certain restrictions, like those against higher derivatives in the lagrangian for quantized GR
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