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How do I properly use Ricci calculus in this example?

  1. Jul 19, 2016 #1
    upload_2016-7-19_15-25-43.png

    Do I substitute [itex]A_\mu + \partial_\mu \lambda[/itex] everywhere [itex]A_\mu[/itex] appears, then expand out? Do I substitute a contravariant form of the substitution for [itex]A^\mu[/itex] as well? (If so, do I use a metric to convert it first?)

    I’m new to Ricci calculus; an explanation as to the meaning of raised and lowered indices here would be greatly appreciated. Everything I've found online so far has been (unnecessarily, I feel) complicated.
     
  2. jcsd
  3. Jul 19, 2016 #2
    This is what I've tried so far. Any suggestions? Was my justification for step (1) correct?

    upload_2016-7-20_8-24-17.png
     
  4. Jul 19, 2016 #3
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