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Noether Currents

  1. Sep 27, 2014 #1
  2. jcsd
  3. Sep 27, 2014 #2
    As Peskin and Schroeder present it, the calculus is essentially that of partial derivatives while treating [itex]\phi[/itex] and [itex]\partial_\mu \phi[/itex] as independent variables. For a given Lagrangian density [itex]\mathcal{L}[/itex], he defines the current in eq. (2.12). However, the current depends on the symmetry at hand, which enters through the [itex]\mathcal{J}^\mu[/itex] term, defined on the previous page.

    If this still looks too opaque, do you remember the treatment of Noether's theorem in classical mechanics of particles?
  4. Sep 28, 2014 #3
    No, I didn't learn it in my classical mechanics subject.

    My doubt is how it get those results for the currents. I tried to do the calcs but I get different results.
  5. Sep 28, 2014 #4
    Ok... To be honest, that is a bit of a red flag! QFT is a tricky subject in its own right, but it relies heavily on classical mechanics. So you may want to pick up a good book and learn Lagrangians, variational calculus and Noether's theorem properly as soon as possible. Otherwise I think you may be in for a rough ride.

    Could you show your work, say for the [itex]\mathcal{L}=\left( \partial_\mu \phi \right)^2[/itex] Lagrangian under the [itex]\phi \rightarrow \phi + \alpha[/itex] transformation? That way it'll be more clear to us where your problems lie.
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