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Mandl and Shaw 5.1

  1. May 14, 2008 #1
    [SOLVED] Mandl and Shaw 5.1

    To show

    [itex]-\frac{1}{2}F_{\mu\nu}F^{\mu\nu} - \frac{1}{2}(\partial_\mu A^\mu)^2 \quad \mathrm{and} \quad -\frac{1}{2}\partial_\nu A_\mu \partial^\nu A^\mu[/itex]

    represent the same Lagrangian it suffices to show that

    [itex]\partial_\nu A_\mu\partial^\mu A^\nu - \partial_\nu A^\nu \partial_\mu A^\mu[/itex] is at most a 4-divergence.

    The trouble is, I have no idea why this would be the case. Is this a matter of utilizing the product rule in some clever way?

    Edit: Yes it is: factor out [itex]\partial_\nu[/itex].
    Last edited: May 14, 2008
  2. jcsd
  3. Oct 25, 2010 #2
    Re: [SOLVED] Mandl and Shaw 5.1

    does anybody have any suggestion to solve 2.4 too?!
  4. Jun 23, 2011 #3
    Re: [SOLVED] Mandl and Shaw 5.1

    Can this be done without using the Lorentz gauge ([itex]\partial_\mu A^\mu = 0[/itex]) or is it necessary imposed ?
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