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Lorentz condition

  1. Oct 4, 2009 #1

    nicksauce

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    1. The problem statement, all variables and given/known data
    Given the Lagrangian
    [tex]
    L = -\frac{1}{2}\partial_{\alpha}A_{\beta}\partial^{\alpha}A^{\beta} + \frac{1}{2}\partial_{\alpha}A^{\alpha}\partial_{\beta}A^{\beta} + \frac{\mu^2}{2}A_{\beta}A^{\beta}[/tex]

    show that A satisfies the Lorentz condition [itex]\partial_{\alpha}A^{\alpha} = 0[/itex].


    2. Relevant equations



    3. The attempt at a solution
    I want to say we can treat [itex]\partial_{\alpha}A^{\alpha}[/itex] as an independent field, and find the appropriate field equations for it, but I'm not sure if that makes sense. Any thoughts?
     
  2. jcsd
  3. Oct 4, 2009 #2

    nicksauce

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    Upon further thought, this seems like a good time to use Noether's theorem...
     
  4. Nov 11, 2010 #3
    Last edited by a moderator: Apr 25, 2017
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