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I'm starting to learn QFT by myself using many references, mostly (QFT for the Gifted Amateur, and Tong's lectures) and both present a proof of Noether's theorem using infinitesimal tranformations, but why is there a reason for that?

It's because is more easy to derive the theorem? In that case, How can I know that the theorem too holds for complete transformations?

Or it's because the theorem holds only for infinitesimals? Does the locality of the fields have something to do with this?

If there is a reference for a proof not using infinitesimal transformations will be appreciated, I'm a bit familiarized with group theory too.

Qmechanic
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Julian Ar.
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    Something being invariant to first order is (typically) weaker than being invariant to all orders. If something is invariant under finite transformations, then it is also invariant under infinitesimal transformations; but the converse is not true. Thus, stating the theorem in terms of infinitesimal transformation leads to a stronger result. – AccidentalFourierTransform Jul 28 '18 at 23:46
  • Possible duplicate: https://physics.stackexchange.com/q/163718/2451 – Qmechanic Jul 29 '18 at 01:08

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