Divergence of the Stress-Energy Tensor

Click For Summary

Discussion Overview

The discussion revolves around the divergence of the Stress-Energy Tensor in the context of Quantum Field Theory, specifically related to Noether's Theorem. Participants are examining a calculation and the transition between two lines in a mathematical derivation.

Discussion Character

  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant expresses difficulty in understanding the transition from line (31) to line (32) in a calculation involving the Stress-Energy Tensor.
  • Another participant suggests that a factor of 1/2 may have been omitted in line (31) regarding the first two terms in the square brackets.
  • A participant agrees with the omission of the factor and proposes that the second term can be rearranged to match the first term, leading to a simplification that cancels with another term in the equation.
  • Subsequent replies confirm the rearrangement and the technique of renaming indices as a valid approach in the derivation.

Areas of Agreement / Disagreement

Participants seem to agree on the potential omission of the factor of 1/2 and the validity of the index renaming technique, but the discussion does not reach a consensus on the overall correctness of the derivation.

Contextual Notes

There may be missing assumptions regarding the specific terms in the calculation, and the dependence on the definitions of the terms involved is not fully explored. The discussion does not resolve the mathematical steps leading to line (32).

Paddyod1509
Messages
10
Reaction score
0
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?

9f06390eaf950b1f7f3fe32ae06e4182.png


Thanks
 
Physics news on Phys.org
It appears they forgot 1/2 in line 31 in the square brackets for the first 2 terms.
 
dextercioby said:
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)?
 
That's right. Just renaming indices summed over, a trick you should know.
 
dextercioby said:
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! :)
 

Similar threads

  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 6 ·
Replies
6
Views
3K
  • · Replies 17 ·
Replies
17
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 13 ·
Replies
13
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 9 ·
Replies
9
Views
3K
  • · Replies 21 ·
Replies
21
Views
4K
  • · Replies 2 ·
Replies
2
Views
2K