In his paper, Zoltan Imre Szabo argues that he can derive Lamb shift without renormalization. In short, he proposes to use De Broglie geometry to remove infinities in QEd.
So, what do you think?
http://arxiv.org/pdf/math-ph/0609027v2.pdf
Dear Dr. Charles Francis, thank you for your answer. Best wishes
The article seems to be very interesting and mathematically clearly satisfies high technical standards. The proposal is that Lamb shift - physically due to radiative corrections - could be derived without playing with infinities. To really understand the article would however require a lot of reading. Renormalization is a physical all established phenomenon and as such need not imply infinities. Maybe the problems of QFTs derive from the use of wrong mathematics. Dirac's bra and ket formalism involving delta functions is very practical but von Neumann algebras (three types of them) might provide an infinity free approach. I believe that also generalisation of particle concept from point like particle to extended object - 3-surface in TGD framework - is necessary. Hyper-finite factors of type II_1 as opposed to factors of type III appearing in algebraic approach to QFTs are natural in TGD framework and might actually reflect the replacement of particle with extended object.
This subject is, by now, of purely historical interest. The relevant, original, work is presented in the book ``Quantum Electrodynamics'' edited by Schwinger, which people interested in the question, are strongly advised to read. Once more, it's not useful to confuse formalism and physics. Different formalisms can and do describe the same physics, in the sense that they give the same answers for the same quantities and there isn't any experiment that can distinguish them.So which one uses is a matter of taste. However certain features can be easier to understand in one formalism than in another and generalizations may be easier to express in one way rather than another (stressed by Feynman in ``The character of physical law''). For insight in the physics Feynman's lectures on QED, http://vega.org.uk/video/subseries/8 are also strongly recommended (there's a book, ``QED: the strange theory of light and matter'', that's the written version). There is a well-defined method for computing the Lamb shift, for seventy years now and what it's called is irrelevant. Szabo's paper is interesting for other issues than the Lamb shift and illustrates, in this regard, another method of calculating the finite result, that's physically relevant. It is a regularization procedure, in the sense that it describes a method for dealing with finite quantities. However there are infinitely many regularization procedures: they all agree on the physical answer and differ by contributions that depend on the details of the procedure. This is well known, of course and was used by Bogoliubov, Parasiuk and Hepp in proving the consistency of perturbative quantum electrodynamics (completed by work of Zimmermann and Lowenstein-cf. Stora's review, http://hal.inria.fr/docs/00/35/49/76/PDF/Contribution_RStora.pdf).
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