Reformulation instead of Renormalizations.

[Bob_for_short]

Dear colleagues,

 

In this thread I would like to share with you my findings in the so called renormalization prescription.

Very briefly, I managed to reformulate the QED in the way that excludes appearing infrared (IR) and ultraviolet (UV) infinities.

 

As you know, in all renormalizable theories one has to carry out the renormalization procedure. In my opinion, such a prescription is nothing but discarding corrections to the fundamental (phenomenological) constants. This is mathematically unacceptable. By chance it may work, but not obligatorily.

 

In my work (http://arxiv.org/abs/0811.4416) I managed to make this as evident as possible. I reduced the problem to 1D classical mechanical (CM) problem that contains in fact all the elements necessary to understand the “nature” of the renormalizations. You will be surprised to see that even in CM one may obtain corrections to the fundamental constants if its equations are written in the so called mixed variables. The mixed variable formulation is as legitimate as any other formulation if your system is made of a “kit” (can be mounted and dismounted). The mixed variable formulation happens to be wrong physically if your system is “welded” (cannot be dismounted into several parts). The latter is the case of the charge-field interaction. The constant renormalization (= correction discarding) is not legitimate mathematically. It is only a good luck that this “works” in some cases.

 

I tried to simplify the problem as much as possible to exclude any doubts and leave the essence apparent. That is why my paper deals mostly with CM problem. I hope the understanding achieved in this work (as well as in http://arxiv.org/abs/0806.2635) will permit to reformulate the particle theories in a more natural way, free from infinities accompanied with wrong justifications in their “doctoring”.

 

We have to recognize that the massive particles and massless fields do not exist separately even in the zeroth approximation but form compound systems. Their QM description is much similar to the QM atomic description: via the center of inertia and relative coordinates. In particular, the electron and the quantized electromagnetic field form an “electronium” where the internal degrees of freedom are described with the photon oscillators. The charge in such a compound system is quantum mechanically smeared (not point-like), just as the negative and positive charges in an atom. This construction leads to much more physical initial approximation of interacting particles and to the sensible results of calculations without appealing to a “shell game”. There is no correction “doctoring” in such an approach. It describes the known QED effects in a natural way. The “free” charge scattering is obligatory inelastic. The inclusive picture (cross section) corresponds to the experimental observations.

 

I invite the researchers to read my simple paper and make remarks if any.

 

Sincerely yours,

 

Bob.

Atom_CEJP.pdf

Reformulation_instead_of_renormalizations.pdf

Edited April 22, 2009 by Bob_for_short

[Bob_for_short]

For copying-and-pasting

π²³ ∞ 0° ~ µ ρ σ ∑ Ω √ ∫ ≤ ≥ ± ∃ … ⋅ θ φ ψ ω Ω α β γ δ ∂ ∆ ∇ ε λ Λ Γ ô

[elas]

Dear colleagues,

 

We have to recognize that the massive particles and massless fields do not exist separately even in the zeroth approximation but form compound systems.

 

As an amateur working only in classical physics I cannot enter into this debate, that said; I came to the above conclusion in my classical work and would be interested to know if your work explains why massless particles cannot exist separately.

[Bob_for_short]

It is an experimental fact. We have to recognize it. Classical mechanical example is given in "Reformulation instead of Renormalizations". Of course, you have to keep in mind that the classical picture is the inclusive quantum mechanical one. I hope you are sufficiently educated to understand a simple QM problem outlined in "Atom as a "Dressed" Nucleus".

 

Bob.

[elas]

It is an experimental fact. We have to recognize it. Classical mechanical example is given in "Reformulation instead of Renormalizations". Of course, you have to keep in mind that the classical picture is the inclusive quantum mechanical one. I hope you are sufficiently educated to understand a simple QM problem outlined in "Atom as a "Dressed" Nucleus".

 

Bob.

 

Lousy education but, according to military examiners (years ago); slightly above average IQ.

I take the 'massless' field to run from the radius of the electric charge to the quantum-mechanical Compton radius, but I will not take up more of your time; instead, I have ordered a book that I hope will lead to a better understanding your paper.

Most forums seem to have gone quiet lately and I shall be most disappointed if others better qualified than myself do not comment on your work, the challenge to existing mathematics is most interesting; thanks for your reply,

jhmar

[Bob_for_short]

One more article on removing divergent corrections by reformulation of the original problem in better terms:

 

On Perturbation Theory for the Sturm-Liouville Problem with Variable Coefficients by Vladimir Kalitvianski, http://arxiv.org/abs/0906.3504.

 

In this article I study different possibilities of analytically solving the Sturm-Liouville problem with variable coefficients of sufficiently arbitrary behaviour. I obtain correct formulas in case of smooth as well as in case of step-wise (piece-constant) coefficients. I show how the problem can be reformulated in order to eliminate big (or divergent) corrections. I build a simple but very accurate analytical formula for calculating the lowest eigenvalue. I advance also new boundary conditions for obtaining more precise initial approximations. I demonstrate how one can optimize the PT calculation with choosing better initial approximations and thus diminishing the perturbative corrections. The consideration is made on a physical level of rigour. "Renormalizations" or "dressing" are discussed in Appendix 4.