- #1
spookyfish
- 53
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Hi,
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
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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