Hi I am re-reading Srednicki's QFT.(adsbygoogle = window.adsbygoogle || []).push({});

In chapter 58,

he points out that the Noether current $$ j^\mu=e\bar{\Psi}\gamma^\mu\Psi$$ is only conserved when the fields are stationary, which is obvious from the derivation of the conservation law.

Meanwhile he assumes that $$\partial _\mu j^\mu=0$$ always holds in deriving the free photon propagator in ch. 56-57

However, he then suggests that "This issue can be resolved" by defining the U(1) gauge transformation.

But I don't see how this solves the issue.

I tried to use the gauge transformation in

$$\partial _\mu j^\mu (x)=\delta \mathcal{L}(x)-(\delta S/\delta\psi_a(x)) \delta\psi_a(x)$$

but I only got trivial result 0 = 0. (well the above equation is an identity so I don't expect otherwise.)

Can anyone tell me what precisely what Srednicki means here?

Thanks a lot

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# Srednicki 58: EM current conservation & Gauge Symmetry

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