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

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Discussion Overview

The discussion revolves around the setup of the stress-energy tensor (SET) for an electron subjected to an electric field that causes it to oscillate. Participants explore the theoretical framework and challenges associated with defining the SET for a point particle in an external field, particularly in the context of general relativity (GR).

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Homework-related

Main Points Raised

  • One participant inquires about the setup of the stress-energy tensor for an oscillating electron in an electric field.
  • Another participant notes that a point particle does not have a stress-energy tensor in the traditional sense, suggesting the use of delta functions to represent it.
  • This second participant argues that a consistent formulation of the SET would require including the stress-energy of the field and constructing a charge-current 4-vector, alongside solving Maxwell's Equations.
  • A beginner participant expresses a lack of understanding of the stress tensor and seeks to solve related problems.
  • There is a request for clarification on which theory the beginner is studying, with a suggestion that the problem is not commonly encountered in standard relativity textbooks.
  • The beginner clarifies they are working from general relativity sources, including Misner and various online lectures, and mentions that the problem was a construct of their imagination.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the feasibility of defining a stress-energy tensor for a point particle in an electric field. There are differing views on the necessity of including the field's stress-energy and the complexity of the problem.

Contextual Notes

The discussion highlights limitations in defining the stress-energy tensor for point particles and the need for additional theoretical constructs, such as charge-current 4-vectors and solutions to Maxwell's Equations. The problem's complexity is noted, as it is not typically addressed in standard relativity exercises.

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

PeterDonis said:
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.
 

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