Divergence of the Stress-Energy Tensor

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SUMMARY

The discussion focuses on the divergence of the Stress-Energy Tensor within the context of Quantum Field Theory, specifically referencing Noether's Theorem. Participants clarify a calculation error regarding the missing factor of 1/2 in line 31 of a derivation. The conversation emphasizes the importance of index renaming as a technique for simplifying expressions, leading to the conclusion that the second term in the square brackets can be rearranged to facilitate the transition from line 31 to line 32.

PREREQUISITES
  • Understanding of Quantum Field Theory concepts
  • Familiarity with Noether's Theorem
  • Knowledge of tensor calculus
  • Experience with mathematical manipulation of equations
NEXT STEPS
  • Study the derivation of Noether's Theorem in Quantum Field Theory
  • Learn about the properties and applications of the Stress-Energy Tensor
  • Explore techniques for index manipulation in tensor equations
  • Review common mistakes in tensor calculations and how to avoid them
USEFUL FOR

Students and researchers in theoretical physics, particularly those studying Quantum Field Theory and tensor calculus, will benefit from this discussion.

Paddyod1509
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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
 
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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! :)
 

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