I Stress Energy Tensor for Oscillator: Setup for Electron in E-Field

[Devin]

How would one go about setting up the stress energy tensor for a particle, say an electron subjected to electric an electric field that makes the particle oscillate with frequency \omega?

 

[PeterDonis]

How would one go about setting up the stress energy tensor for a particle

Strictly speaking, a point particle doesn't have a stress-energy tensor. The SET describes a continuous distribution of matter/energy. However, you can finesse this by using delta functions, as shown here:

https://en.wikipedia.org/wiki/Stress–energy_tensor#Stress.E2.80.93energy_in_special_situations

However, as that article says, the SET given there is for a non-interacting particle. I don't think you can consistently formulate an SET for just a charged particle in an electric field. You would have to include the stress-energy in the field as well, and to be self-consistent you would have to also construct a charge-current 4-vector to describe the particle and solve Maxwell's Equations, and verify that your solution of Maxwell's Equations gave you the fields you used to construct the SET.

It would help to have more information about why you want to do this.

 

[Devin]

I'm just in my beginning stages of learning the theory. I've derived just about everything, but i don't understand the stress tensor, or how to construct it. I would like to be able to solve problems, and this is one that came to mind.

 

[PeterDonis]

I'm just in my beginning stages of learning the theory.

What theory? SR? GR? What sources have you used? How did this particular problem occur to you?

I'm asking because the problem you're asking about is not one that is normally encountered as an exercise in relativity textbooks; they usually ask about stress-energy tensors that are much easier to define and work with, such as the SET of a perfect fluid.

 

[Devin]

GR is what I'm working out of. Misner, Lewis, and plenty of YouTube lectures. It was simply a construct that I had imagined...

What theory? SR? GR? What sources have you used? How did this particular problem occur to you?

I'm asking because the problem you're asking about is not one that is normally encountered as an exercise in relativity textbooks; they usually ask about stress-energy tensors that are much easier to define and work with, such as the SET of a perfect fluid.