Four divergence of stress energy tensor

[decerto]

Homework Statement

Hi, I'm trying to show the four divergence of the stress energy tensor of the sourceless klein gordon equation is zero. I got to the part in the solution where I am left with the equations of motion which is identically zero and 3 other terms.

I managed to find a solution online

See equation (30) to (32) in this pdf for where I am stuck

Firstly I have no idea where the factor of a half goes from (30) to (32) and secondly if it is legitimately gone for some reason, then the second and third term in (31) are equal and opposite which leaves you with just the 4th term, how does this equal to zero?

Homework Equations

In the hyperlink

The Attempt at a Solution

In the hyperlink

 

[George Jones]

Can you go from (30) to (31), i.e., can you show that the stuff after the first minus sign in (30) equals the stuff after the first minus sign in (31)?

 

[dextercioby]

Does the product rule seem familiar to you? If so, start by computing $\partial_{\mu}\phi^2$

 

[decerto]

Its fine, I got a reply on a different forum, the 1/2 should not have dissapeared, that is what was confusing me.