Divergence of the Stress-Energy Tensor

In summary, the conversation is about a student studying Quantum Field Theory and having difficulty understanding a calculation involving Noether's Theorem. They discuss a possible mistake in line 31 and how to rearrange the terms to get the correct result in line 32. The other person mentions a trick they should know for renaming indices and the student expresses gratitude for the help.
  • #1
Paddyod1509
10
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
 
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  • #2
It appears they forgot 1/2 in line 31 in the square brackets for the first 2 terms.
 
  • #3
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)?
 
  • #4
That's right. Just renaming indices summed over, a trick you should know.
 
  • #5
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! :)
 

FAQ: Divergence of the Stress-Energy Tensor

1. What is the stress-energy tensor?

The stress-energy tensor is a mathematical object used in general relativity to describe the distribution of matter and energy in a given space. It is a rank-2 tensor that contains information about the mass, energy, momentum, and stress of a system.

2. What does the divergence of the stress-energy tensor represent?

The divergence of the stress-energy tensor represents the rate of change of the stress and energy flow in a given space. It describes how the energy and momentum are being redistributed within a system.

3. How is the divergence of the stress-energy tensor related to the equation of motion?

The divergence of the stress-energy tensor is directly related to the equation of motion in general relativity, known as the Einstein field equations. It describes how the curvature of spacetime is affected by the distribution of matter and energy.

4. What are the physical implications of a non-zero divergence of the stress-energy tensor?

A non-zero divergence of the stress-energy tensor indicates that there is a non-uniform distribution of energy and momentum in a given space. This can have physical consequences such as the generation of gravitational waves or the formation of black holes.

5. How is the divergence of the stress-energy tensor calculated?

The divergence of the stress-energy tensor is calculated using the principles of differential geometry and tensor calculus. It involves taking the partial derivatives of the components of the tensor with respect to the coordinates of the space in which it is defined.

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