# Four divergence of stress energy tensor

1. Nov 25, 2014

### decerto

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

2. Relevant equations

3. The attempt at a solution

2. Nov 25, 2014

### George Jones

Staff Emeritus
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)?

3. Nov 25, 2014

### dextercioby

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

4. Nov 25, 2014

### decerto

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