

Preprint 17/2008
De Broglie geometry eliminating the infinities of QED; An exact derivation of the Lamb shift formula in the normal case
Zoltan I. Szabo
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Submission date: 13. Feb. 2008
Pages: 36
Bibtex
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Abstract:
This paper evolves a new non-perturbative theory by which the problem
of infinities appearing in quantum physics can be handled. Its
most important application is an exact derivation of the Lamb
shift formula by using no renormalization. The
Lamb shift experiment (1947) gave rise to one of the greatest
challenges whose explanation brought the modern
renormalization technique into life. Since then this is the only tool for
handling these infinities. The relation between this
renormalization theory and our non-perturbative theory is also
discussed in this paper.
Our key insight is the realization that the
natural complex Heisenberg group representation splits the Hilbert space,
,
of complex valued
functions defined on an even dimensional Euclidean
space into irreducible subspaces
(alias zones) which are invariant also under the action
of the Landau-Zeeman operator.
After a natural modification,
also the Coulomb operator can be involved into this zonal theory.
Thus these zones can be
separately investigated, both from
geometrical and physical point of view.
In the literature only the zone
spanned by the holomorphic polynomials has been investigated so far.
This zone is the well known Fock space.
This paper explicitly
explores also the ignored (infinitely many) other zones.
It turns out that
quantities appearing as infinities on the total Hilbert space
are finite in the zonal setting. Even the zonal Feynman integrals
are well defined. In a sense,
the desired finite quantities are provided here by an extended
particle theory where these extended objects show up also on the
rigorously developed mathematical level. Name de Broglie geometry
was chosen to suggest this feature of the zonal theory.