Understanding EM Stress Energy Tensor: Sources and Current Density

In summary, the conversation is about trying to obtain the EM stress energy tensor and questioning if the equation found online is correct with or without sources. The discussion also mentions the possible inclusion of a current density term and suggests looking at 't Hooft's notes for more information. Finally, it is confirmed that the equation found online is without any sources and that a term proportional to the product of AJ is expected to be included.
  • #1
tim_lou
682
1
I've been trying to obtain the EM stress energy tensor... but I'm not sure if what I got is correct.

In all the websites I googled, I found
[tex]T^{\mu\nu} =- \frac{1}{4}g^{\mu\nu} F^{\alpha\beta}F_{\alpha\beta} + F^{\mu}\,\!_{\lambda}F^{\nu\lambda}[/tex]

However, is this with the sources or without the sources? Seems to me that this is what I would get for a Lagrangian without current. what happens if I add a current density?

I just need a quick answer... I can't seem to find anything online.
 
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  • #2
Try 't Hooft's notes, Eq. 10.9
http://www.phys.uu.nl/~thooft/lectures/genrel.pdf
 
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  • #3
thanks, got my answer, indeed that form above is without any source. A term proportional to the product of AJ are included, as expected.
 

Related to Understanding EM Stress Energy Tensor: Sources and Current Density

1. What is an EM Stress Energy Tensor?

The EM Stress Energy Tensor is a mathematical representation of the energy and momentum of an electromagnetic field. It describes the distribution of energy and momentum in space and time for a given electromagnetic field.

2. What are the sources of the EM Stress Energy Tensor?

The sources of the EM Stress Energy Tensor are the electric and magnetic fields. These fields can be caused by moving charges, changing electric fields, or changing magnetic fields.

3. How is the EM Stress Energy Tensor calculated?

The EM Stress Energy Tensor is calculated using Maxwell's equations, which describe the behavior of electromagnetic fields. It involves calculating the electric and magnetic fields at each point in space and time and then using those values to calculate the energy and momentum at that point.

4. What is the relationship between the EM Stress Energy Tensor and current density?

The EM Stress Energy Tensor is directly related to the current density, as it includes terms for the flow of charge and the change in flow of charge over time. Current density is an important factor in determining the energy and momentum of an electromagnetic field.

5. Why is understanding the EM Stress Energy Tensor important?

Understanding the EM Stress Energy Tensor is important for many reasons. It allows us to accurately describe and predict the behavior of electromagnetic fields, which is crucial in many scientific and technological applications. It also helps us better understand the fundamental nature of energy and momentum in the universe.

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