# Q on Jackson. Lorentz force modification for radiation?

1. Sep 22, 2009

### Peeter

Reading Jackson this morning, where it was stated that the Lorentz force equations:

$$\frac{dU^\alpha}{d\tau} = \frac{e}{mc} F^{\alpha\beta} U_\beta$$

are sufficient to describe the motion of a charged particle in an external field, neglecting the effects of radiation.

That radiation qualifer suprised me. What is the modification of the Lorentz force equation (or Lagrangian) that correctly models radiation too?

2. Sep 22, 2009

### Bob_for_short

Isn't it given in Jackson book later on?

3. Sep 22, 2009

### Peeter

If it is I wouldn't know yet. The qualification is made in passing, and there's no hint of what to look for. Does the corrected force law have a name that I could look for in the index?

4. Sep 22, 2009

### Count Iblis

Jackson (or for that matter any other textbook) does not give a rigorous derivation; this was one of big problems of classical electromagnetism: How to take into account the interaction of a point charge with its ow electromagnetic field in a rigorous way?

The solution to this problem is given here:

http://arxiv.org/abs/0905.2391

5. Sep 22, 2009

### Bob_for_short

Yes, there is a name, it is the Abraham-Lorentz force. Try Wikipedia.

6. Sep 22, 2009

### Staff: Mentor

In my old 2nd edition of Jackson, the Abraham-Lorentz force is in chapter 17 which discusses radiation damping.

7. Sep 22, 2009

### Peeter

thanks for the paper and the name.