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I am wondering if an extension of Noether theorem to supergroups exists. In particular the analogy with the usual case should be that supersymmmetries are in 1 to 1 correspondence to certain "currents" whose charge is the supersymmetric spinor charge $Q_{\alpha}$.

Has this topic been studied at all?

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Google readily returns lecture notes on exactly this topic: cds.cern.ch/record/444907/files/0006198.pdf. I suggest you start reading there! –  Danu Feb 8 at 15:58
    
That link is for a dissertation by Alfredo Iorio, not lecture notes (big difference between the two). Also, link only answers do not make good answers. –  Kyle Kanos Feb 8 at 18:48

1 Answer 1

I) First it should be stressed that Noether's theorem is not really about Lie groups but only about Lie algebras, i.e., one just needs $n$ infinitesimal symmetries to deduce $n$ conservation laws.

II) Secondly, it is straightforward to check (by recalling the proof of Noether's theorem) that Noether's theorem generalizes to supernumber-valued variables, transformations, currents, and charges.

Examples of Grassmann-odd symmetries include BRST symmetry and Poincare super-symmetry.

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