How is the Relativistic Larmor Formula Derived Using Dot Products?

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Discussion Overview

The discussion focuses on the relativistic generalization of the Larmor formula, specifically seeking a derivation that utilizes dot products rather than covariance. Participants express interest in finding resources that detail the integral involved in this derivation step by step.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant requests resources for the relativistic Larmor formula, emphasizing the need for a derivation involving dot products.
  • Another participant suggests a lecture that contains a derivation but notes it is in German and questions if it meets the request.
  • A participant acknowledges the provided resource but clarifies that they need assistance with evaluating the integral, which involves multiple dot products due to a triple cross product.
  • Another participant references a specific equation from a different source that shows the integral worked out step by step, raising a question about the relationship between the angles involved and the dot product of acceleration and unit vector.

Areas of Agreement / Disagreement

Participants do not appear to reach consensus on the best resource or method for deriving the formula, and multiple competing views on the derivation process and resources remain present.

Contextual Notes

Participants express uncertainty regarding the specific steps involved in evaluating the integral and the implications of the angles in the dot product, indicating potential limitations in their understanding or the resources provided.

Who May Find This Useful

This discussion may be useful for those interested in advanced electrodynamics, particularly in the context of relativistic effects and mathematical derivations involving dot products.

nos
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Hi all,

Does someone know where to find the relativistic generalization of the larmor formula? I'm interested in the integral that involves a lot of dot products. So not the derivation that uses covariance to arrive at the formula.

Are there any articles or books available that work out this integral step by step?

Thank you very much.
 
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nos said:
Does someone know where to find the relativistic generalization of the larmor formula? I'm interested in the integral that involves a lot of dot products.

This (http://www.ita.uni-heidelberg.de/research/bartelmann/Lectures/elektrodynamik/edynamik.pdf ) lecture has a derivation of the relativistic Larmor formula I once comprehended - around page 159. There are two catches:

1) It's in German (but many formulae, so you might get it)
2)I don't know if it is the kind of proof you requested.

If you have problems in one or two steps, I shall help translating.
 
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Hi, thank you for replying and its what I've been looking for. Except that I know that the integrated power gives this result. I need to know how to evaluate this integral. It involves a lot of dot product because of the triple cross product.
 
It's equation 12.70 integrated over all solid angles that give the total power radiated.
 
In http://www.phys.lsu.edu/~jarrell/COURSES/ELECTRODYNAMICS/Chap14/chap14.pdf (page 14)it shows the integral and it is worked out step by step. They set the angle between velocity and unit vector =Theta, and angle between acceleration and velocity = Theta(0). Does this mean that the dot product of acceleration and unit vector= acceleration * cos(theta(0)-theta))? Sorry for not using math formulas, I am at work on my mobile and doesn't allow formulas.
 

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