How do Noether's theorems apply to field theory and discontinuous symmetries?

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akai_ma
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ok so I understand the general idea of Emmy Noether's theorems, for every differentiable continuous symmetry there is a correlated conservation. The classical formulation seems simple enough, but the field theory formulation seems nasty. I have been through electrodynamics and quantum mechanics. So my question is this:
Where can I find an in depth understadable formulation of Noether's theorems for field theory?
Also from what I've read the theorems only work for continuous symmetries. What about discontinuous symmetries like parity?
 
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