In fact this is Lenard Wiechert potential in D dimension. Usually it's written as sum of some terms, depending on D and isn't useful for differentiation. More advanced form differs for odd and even D.
Fourier transform is quite straightforward, in many cases. ``Most suitable'', however, isn't very meaningful, since it depends on the details of the problem. Learning the technical aspects for oneself is more important than performing a poll. There aren't ``more advanced'' or ``less advanced'' forms, simply ``useful'' forms, for doing the calculations. One gets credit for the result, in ``real life'' situations, not for the method by which its obtained.
To have unified expression for odd and even D the best form I found in the literature is:
K(r,t)=const*(r2-t2+i*0)1-D/2, where you should use distributions.
Eugene> the best form I found
How does that form help you understand the basic fact that you can turn off the light in odd space dimensions, but not in even space dimensions? As Stam points out, what is 'best' will depend on which problem you want to elucidate.
Eugene
I don't at all deny the usefulness of your expression, which I have had the occasion to use profitably -- in combination with the method of images one learns about in introductory electrostatics -- for Casimir effect calculations. I only wanted to warn you about the notion of best; you should not lock yourself out from other possible representations, and the added insights they may give.
And don't forget which PDE, with which boundary conditions, is solved by your solution; it is not only a question of how to represent the solution, but what it is the solution of.
Kåre
Thank you for your comments. I remember, that I need to add solution of homogeneous equation. Did you try to find selfenergy of pointlike charge in D-dimensions, btw?
Eugene> Did you try to find selfenergy of pointlike charge in D-dimensions?
I have for sure tried in more than one way! The result is always infinite; the trick is to subtract the infinite part in a sensible and invariant way, so that one may reliably calculate energy differences .
The best classical treatment of such problems is (in my opinion) the work by Julian Schwinger: Found.Phys. 13 (1983) 373-383, DOI: 10.1007/BF01906185, although the model he analyzes is not realistic in every aspect.
Usually phenomenon of race-acceleration is deriving as third positive root of ODE. But if you will write "correct" equation, you will have negative root with no race-acceleration. Details are in my "working materials". And sense of third derivative is - one more degree of freedom is due to electromagnetic potentials.
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