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# Quantum theory , variation of S is zero, integrate by parts watch

1. 1. The problem statement, all variables and given/known data

I am trying to show the second equality , expressing all as a total derivative (I can then show that )

2. Relevant equations
See above

3. The attempt at a solution

So the term is pretty obvious, simply using the chain rule. It is the first term I am stuck on.

So looking by the sign, it looks like we have done integration by parts twice.

My working so far is to go by parts initially as:

to get, since we are allowed to assume vanishing of the field at inifnity:

I am now stuck of what to do, I can't see a move that will get the desired expression for a choice of integration by parts, which makes me question whether this was the correct first move to make.

2. (Original post by xfootiecrazeesarax)
1. The problem statement, all variables and given/known data
I had a go at this, but got horribly lost in a sea of co- and contra- four-gradients. You could try posting either on physicsforums.com or physics,stackexchange.com, where there will certainly be people more able to help with this.

The layout and presentation of your problem and working is very nice and clear, BTW.

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Updated: January 12, 2017
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