# How do I properly use Ricci calculus in this example?

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1. Jul 19, 2016

### jdbbou

Do I substitute $A_\mu + \partial_\mu \lambda$ everywhere $A_\mu$ appears, then expand out? Do I substitute a contravariant form of the substitution for $A^\mu$ 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. Jul 19, 2016

### jdbbou

This is what I've tried so far. Any suggestions? Was my justification for step (1) correct?

3. Jul 19, 2016