- #1

binbagsss

- 1,265

- 11

## Homework Statement

Does ##x_p\partial_v\partial_u-x_v\partial_p\partial_u=0##

## Homework Equations

I need this to be true to show a poincare algebra commutator.

We have just shown that ##[P_u, P_v] =0 ##, i.e. simply because partial derivatives commute.

Where ##P_u=\partial_u##

## The Attempt at a Solution

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I'm guess it's using that partial derivatives commute and renaming the ##v## and ##p## for each other, however I'm a bit confused with this, because, I know this isn't really the context here, but these are free indicies not dummy indices, i..e not an index summing over, so I'm a bit unclear how you could simply rename.

Many thanks