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Main Question or Discussion Point
It is certainly interesting that the Quantum Field Theories like QED can be reformulated so that no divergences appear at all. Usually the ultraviolet divergences are "cured" with renormalizations. But recently I posted a paper (http://arxiv.org/abs/0811.4416) with the following abstract [1]:
In this article I show why the fundamental constants obtain perturbative corrections in higher orders, why the renormalizations work and how to reformulate the theory in order to avoid these technical and conceptual complications. I demonstrate that the perturbative mass and charge corrections are caused exclusively with the kinetic nature of the interaction Lagrangian. As soon as it is not purely quantum mechanical (or QFT) specific feature, the problem can be demonstrated on a classical twobody problem. The latter can be solved in different ways, one of them being correct and good for applying the perturbation theory (if necessary) and another one being tricky and awkward. The first one is physically and technically natural  it is a centerofinertiaandrelativevariable formulation. The second one  a mixed variable formulation  is unnecessarily complicated and leads to the mass and "charge" corrections even in the Newtonian mechanics of two bound bodies. The perturbation theory in QFT is factually formulated in the mixed variables  that is why it brings corrections to the fundamental constants. This understanding opens a way of correctly formulating the QFT equations and thus to simplify the QFT calculations technically and conceptually. For example, in scattering problems in QED it means accounting exactly the quantized electromagnetic field influence in the free in and out states of charged particles so no infrared and ultraviolet problems arise. In bound states it means obtaining the energy corrections (the Lamb shift, the anomalous magnetic moment) quite straightforwardly and without renormalizations.
The most important findings are:
1. The energymomentum conservation law can be preserved in QED in a physically and mathematically natural way rather than in the frame of selfaction ansatz with inevitable renormalizations.
2. The Novel QED has the correct classical limit where the radiation is unavoidably taken into account (the inclusive picture) rather than neglected.
3. The electron ( or more generally, a charge) and the quantized electromagnetic field form a compound, in a certain sense "welded" rather than "mountabledismountable" system. I call it an electronium. Its quantum mechanical description is quite similar to the atomic one [2]. In particular, photons are just excited electronium states. No constant renormalizations are necessary in such an approach, no divergences appear.
4. I propose to construct the other "gauge" theories in the same spirit  as theories where compound systems (fermioniums) interact with possible exciting their internal (relative) degrees of freedom ("gauge" bosons). The simplest physical analogy to that is the fast atom1atom2 scattering at large angles when only nucleus1nucleus2 (Coulomb or not) potential is important and the final atomic states are excited [2].
I hope this approach deserves attention and a further development.
Vladimir Kalitvianski.
[1] Reformulation instead of Renormalizations, http://arxiv.org/abs/0811.4416.
[2] Atom as a "Dressed" Nucleus, Central European Journal of Physics, V. 7, N. 1, pp. 111, (2009) by Vladimir Kalitvianski, (available also at http://arxiv.org/abs/0806.2635).
In this article I show why the fundamental constants obtain perturbative corrections in higher orders, why the renormalizations work and how to reformulate the theory in order to avoid these technical and conceptual complications. I demonstrate that the perturbative mass and charge corrections are caused exclusively with the kinetic nature of the interaction Lagrangian. As soon as it is not purely quantum mechanical (or QFT) specific feature, the problem can be demonstrated on a classical twobody problem. The latter can be solved in different ways, one of them being correct and good for applying the perturbation theory (if necessary) and another one being tricky and awkward. The first one is physically and technically natural  it is a centerofinertiaandrelativevariable formulation. The second one  a mixed variable formulation  is unnecessarily complicated and leads to the mass and "charge" corrections even in the Newtonian mechanics of two bound bodies. The perturbation theory in QFT is factually formulated in the mixed variables  that is why it brings corrections to the fundamental constants. This understanding opens a way of correctly formulating the QFT equations and thus to simplify the QFT calculations technically and conceptually. For example, in scattering problems in QED it means accounting exactly the quantized electromagnetic field influence in the free in and out states of charged particles so no infrared and ultraviolet problems arise. In bound states it means obtaining the energy corrections (the Lamb shift, the anomalous magnetic moment) quite straightforwardly and without renormalizations.
The most important findings are:
1. The energymomentum conservation law can be preserved in QED in a physically and mathematically natural way rather than in the frame of selfaction ansatz with inevitable renormalizations.
2. The Novel QED has the correct classical limit where the radiation is unavoidably taken into account (the inclusive picture) rather than neglected.
3. The electron ( or more generally, a charge) and the quantized electromagnetic field form a compound, in a certain sense "welded" rather than "mountabledismountable" system. I call it an electronium. Its quantum mechanical description is quite similar to the atomic one [2]. In particular, photons are just excited electronium states. No constant renormalizations are necessary in such an approach, no divergences appear.
4. I propose to construct the other "gauge" theories in the same spirit  as theories where compound systems (fermioniums) interact with possible exciting their internal (relative) degrees of freedom ("gauge" bosons). The simplest physical analogy to that is the fast atom1atom2 scattering at large angles when only nucleus1nucleus2 (Coulomb or not) potential is important and the final atomic states are excited [2].
I hope this approach deserves attention and a further development.
Vladimir Kalitvianski.
[1] Reformulation instead of Renormalizations, http://arxiv.org/abs/0811.4416.
[2] Atom as a "Dressed" Nucleus, Central European Journal of Physics, V. 7, N. 1, pp. 111, (2009) by Vladimir Kalitvianski, (available also at http://arxiv.org/abs/0806.2635).
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