Hi,(adsbygoogle = window.adsbygoogle || []).push({});

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

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Noether current

**Physics Forums | Science Articles, Homework Help, Discussion**