- #1

binbagsss

- 1,266

- 11

## Homework Statement

Hi,

Please see attached.

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

## Homework Equations

See above

## The Attempt at a Solution

So the ## m ## 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:

##w=\partial^{u}\phi ##

##\partial w = \partial_{v}\partial^{u} \phi ##

## \partial z = \partial_{u}\partial_{v} \phi ##

## z= \partial_{u} \phi ##

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

## - \int \partial_{u} \phi ( \partial_{v} \partial^{u} \phi ) ##

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.

Many thanks in advance.