Sidney Coleman's argument for a hyperbolically accelerated electron radiating

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john mcandrew

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Oct 24, 2020, 3:02:47 AM10/24/20
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Sidney Coleman wrote a report in 1961 that derived the LAD equation for a classical electron using what was then 'modern theory':

https://www.rand.org/pubs/research_memoranda/RM2820.html

I've tried to copy his diagram below which formats OK using classic Google groups but not in the newer, current version. On page 35 he writes:

"-----"
If we remember that in Maxwellian dynamics, the radiation field is given by the difference of the advanced and retarded fields, it is easy to see that the electron radiates.

\ |t /*
\ | /*
\ | /.
\ | /
\ | / *
\ \ | / /
_______________\__\ /__* ___/__________x
\ / \ * /
/ | \ /
/ \| \ */
/ | \/.
/ |\ /\
/ | \/ \*
/ | /\P \*
|/ \
/ \
/| \
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The figure shows the world line of an electron undergoing hyperbolic acceleration. The past light cone from the point P does not interact with the electron worldline, so the retarded potential vanishes; the future light cone intersects it once, so the advanced potential doesn't. Thus there is a radiation field at P."
"-----"

I don't agree with this. The past light cone of the observation point P not intersecting with the electron's world line means the retarded field at P is undefined rather than being zero, and hence the radiation field there is also undefined.


Thanks in advance for any comments.

J McA
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