[FOM] Question about theoretical physics

[Joe Shipman]

Neumaier writes:
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I have given in my FAQ detailed references to the relevant publications. See
  Is QED consistent? (from Chapter B5)
  http://www.mat.univie.ac.at/~neum/physfaq/physics-faq.html
They give an amount of details considered to be adequate by the physics community. To repeat the calculations based on these publications should be possible for every physicist trained in quantum field theory, prepared to study the background literature, and diligent enough in high performance programming. But it is a lot of work, and I never tried. It is highly specialized work, and checked only by highly specialized people.
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That page contains enough details and references that I believe your last sentence, and I congratulate you for stating the issues so clearly.  The referenced paper by Passera is particularly well-organized and carefully written.

I would not go quite so far as to say there is an explicit algorithm that gives a value for arbitrary orders of approximation; rather, at each order of approximation ad hoc choices are made to speed up and simplify the calculation, but it is clear that a theoretical algorithm exists. 

The situation is comparable to how calculations used to be done in homotopy theory: although a theoretical algorithm existed, it was impractically slow, and calculations were done in an ad hoc way with various exact sequences, which was claimed to be algorithmic but was not in fact an effective procedure in the formal sense. Francis Sergeraert cleared this up in the 90's by developing "effective homotopy theory", but QED has not yet reached that stage.

--JS
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