I can not get this Noether current from the Lagrangian of L = i Psi-bar gammamu(dmu+igTaAmua) Psi - 1/4 Fmu nua dagger Fmu nua
The Noether current supose should yield as is showed in the picture IMG_20160722_112249.jpg
Reference: An introductory Course of Particle Physics. Palash B. Pal. pages 300-306
See lecture notes by Mathew Schwarz, http://isites.harvard.edu/fs/docs/icb.topic1146666.files/IV-1-YangMills.pdf, eqn. (80), which agrees with yours except that there is a relative sign between two terms of the Noether's current.
An interesting point is that the associated conserved charge Qa=∫d3x Ja0 depends on the choice of gauge. Consequently in a theory like QCD there is no such thing as a classical current made out of quarks in analogy to the case in QED where electrons constitute a gauge invariant electric current.
In any theory, that's invariant under non-abelian transformations, the correspondining current is covariantly conserved, not invariantly conserved, as is the case for an abelian theory. However the statement that there isn't a classical current isn't correct-this Lagrangian is classical, after all (and it doesn't contain any gauge fixing term, incidentally, so the statement that the charge depends on any gauge requires elaboration). It's not true that the *fact* that the charge is conserved at all, depends on the choice of gauge, either. One way to realize this is by showing that, for any gauge theory, the invariance under local transformations can be expressed as the invariance under global transformations, that expresses that, for any given gauge fixing term, the effects of unphysical fields, whose contributions cancel those of the unphysical temporal and longitudinal components of the gauge fields, doesn't depend how the unphysical fields are introduced, nor how the gauge is fixed (These are called Becchi-Rouet-Stora-Tyutin, or BRST, transformations).
A corresponding statement is true in general relativity, where the energy-momentum tensor, which is the current obtained when studying transformations that are local translations, is covariantly conserved-it's invariantly conserved only in flat spacetime.
To get back to the question, one gets the Noether current the usual way: by writing down the variations of the fields under transformations with parameters that depend on the spacetime point and expressing the variation of the Lagrangian, up to total derivatives, as the product of the parameters and the divergence of the current. What's the problem?
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