Divergence of the Stress-Energy Tensor

[Paddyod1509]

Im studying Quantum Field Theory as part of my undergraduate course, and am currently looking at Noether's Theorem which has led me to the following calculation of the divergence of the Stress-Energy Tensor. I'm having difficulty in seeing how we get from line (31) to line (32). Is the 2nd term in the square brackets zero? if so, why?

Thanks

 

[dextercioby]

It appears they forgot 1/2 in line 31 in the square brackets for the first 2 terms.

 

[Paddyod1509]

It appears they forgot 1/2 in line 31 in the square brackets for the first 2 terms.

Thanks, i thought this could be the case. Then inside the square brackets I am assuming we can rearrange the second term so that the first and second term are the same. so we get 1/2*[...] + 1/2*[...] = [...]. and this [...] cancels with the second term of the whole line, resulting in line (32)?

 

[dextercioby]

That's right. Just renaming indices summed over, a trick you should know.

 

[Paddyod1509]

That's right. Just renaming indices summed over, a trick you should know.

indeed, a trick I am quickly beginning to learn! Thanks for your help! :)