co se clovek vsechno nedovi..
>>>> When an isolated electron emits a photon, the photon must be reabsorbed.
>>>> Since the electron is isolated, the photon must be reabsorbed by the
>>>> emitting electron - that is a definitional truism, or the electron would
>>>> not be isolated. This is represented as a loop integral. Normally that
>>>> is thought to diverge. Actually it does not diverge. If one does not
>>>> piss all over basic mathematics which one should learn as a first year
>>>> undergraduate, and does the calculation properly this loop integral is
>>>Why do you say so? The electron self-energy loop integral is infinite.
>>>This is shown in every QFT textbook.
>>Every QFT textbook bar one, afaik. The one being Scharf, Finite QED.
>>> Or I don't understand you correctly?
>> You understand me correctly. It was fine for Dyson, Feynman, Schwinger
>> to do the calculations in a heuristic manner, which generated
>> divergences. It was even fine for them to deal with the divergences in
>> an ad hoc manner. It is not fine for succeeding generations to follow
>> the same arguments and to fail to straighten them out. As early as the
>> seventies it had been shown by Epstein and Glaser et al that the
>> ultraviolet divergences were to do with elementary errors in analysis,
>> the abuse of Wick's theorem, which effectively means the changing of
>> orders of integration where we do not have uniform convergence. I showed
>> the same thing in my own doctoral thesis, albeit a few years later.
>> The fact that this kind of abuse of mathematics will produce nonsensical
>> results has been known for about two hundred years and was well sorted
>> out by the latter half of the C19th. This is taught to first year maths
>> undergraduates. There was some excuse in the early days of qed, but for
>> modern text books like Peskin and Schroeder to produce the same stuff is
>> pure incompetence, imv. Based on this bad mathematics we have whole
>> reams of research into absolute nonsense, from the belief in the Higgs
>> boson, false arguments about renormalisability, the conceptual basis of
>> field theory, through to string theory.
>I refuse to believe that Dyson, Feynman, Schwinger, Schweber, Bjorken,
>Drell, Peskin, Schroeder, Weinberg, ... all made an elementary
An elementary mistake in a sense, but well buried in difficult
mathematics. The fact is that physicists had never had to pay attention
to such issues as uniform convergence when changing the order of
integration. They were always able to argue "this is physical so it must
be finite". That argument does not apply to the mathematical structure
of quantum theory. It should have been quickly recognised that it does
not apply, and the effect of changing the order of integration should
have been examined. It was one of the things I set out to examine in my
own thesis, and it has been examined by others before me. I don't think
there is any excuse for your attitude. For Dyson Feynman and Schwinger
to do a heuristic calculation to get an answer is fine. But to fail to
recognise even after the occurrence of divergence that the calculation
contains a mathematically illegal operation, and fail to analyse the
effect of that operation, that is not fine. That is plain sloppy and
mathematically incompetent. To say that "Feynman did it, so it must be
right" is not science and it is not the way mathematics is done. It is
necessary to construct the theory and the integrals carefully, and to
watch things like orders of integration. In the context of these
calculations, which are quite elaborate, that is much more difficult.
But there is still no excuse for not doing it. Nor is there any excuse
for writing down, as Peskin and Schroeder do, expressions equivalent to
1 + infinity + infinity^2 + ... = 1/(1-infinity) = 0
The effect of that, combined with the attitude "oh you get the right
answer so it must be right" together with hostility towards anyone who
tries to do the maths properly, is the reason why there are very few
mathematically competent theoretical physicists, and the reason why
theoretical physics has been stalled for fifty years.