How is the Relativistic Larmor Formula Derived Using Dot Products?

[nos]

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.

 

[Yuu Suzumi]

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.

 

[nos]

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.

 

[nos]

It's equation 12.70 integrated over all solid angles that give the total power radiated.

 

[nos]

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.