I am confused by various derivations of the Noether current in various text books. However, they either contradict with each other or exist many flaws.(adsbygoogle = window.adsbygoogle || []).push({});

For example, originally I thought the best derivation is at the end of the book of classical mechanics by Goldstein. But I found that in the result eq(13.147) (3rd edition), only global symmetry can be used.

Even in Weinberg's section 7.2, the derivation of the energy-momentum tensor (spacetime translational symmetry), the derivation is quite unreasonable. Suddenly appearing of [tex]\epsilon^\mu\partial_\mu\mathcal{L}[/tex] (this term is usually obtained from the deviation of the measure [tex]d^4x[/tex] in other QFT texts).

Moreover, in Ryder's QFT book, his derivation seems to neglect the difference of two variations (even Weinberg made this mistake I thought):

[tex]\Delta\phi(x) \equiv \phi'(x') - \phi(x)[/tex]

[tex]\delta\phi(x) \equiv \phi'(x) - \phi(x)

where [tex]\left[\Delta,\partial_\mu\right]\neq 0[/tex] while [tex]\left[\delta,\partial_\mu\right] = 0[/tex].

The best derivation I have ever seen is Maggiore's.

Is there anybody agrees with me?

Or is there good and reasonable derivations?

Thanks in advance.

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# Problematic derivations of Noether's theorem

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