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I read about Noether's theorem, which states that if, under a continuous transformation, the Lagrangian is changed by a total derivative

[itex] \delta \cal L = \partial_\mu F^\mu [/itex]

then there is a conserved current

[tex] j^\mu = \frac{\partial \cal L}{\partial(\partial_\mu \phi)}\delta \phi - F^\mu [/tex]

However, I have seen in a different place the formulation that if the action is invariant, then the conserved quantity is:

[tex] \frac{\partial \cal L}{\partial(\partial_\mu \phi)}\delta \phi - T^{\mu \nu}\delta x_\nu [/tex]

where [itex] T^{\mu \nu} [/itex] is the energy-momentum tensor.

Is the second formulation equivalent to the first? or is it a particular case

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# Noether current

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