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As you know, renormalization of equation coefficients is necessary when these (already good) coefficients acquire unnecessary perturbative corrections. Discarding those corrections is the essense of renormalization.

Perturbative corrections to the equation coefficients appear at a certain stage of theory development - when we are trying to make the phenomenological equations even more exact with including known to us, but missing in our equations, physical effects like radiation reaction force.

Our way of theory development is not always successful - we may unintentionally spoil our original equations, i.e., we may include something wrong in the missing term. That is why we encounter disagreement of new solutions with experiment. Sometimes those extra (bad) terms are so simple and evident that their discarding restores the original properties of our approximate equations. However, and this is a good news, we may formulate our theory correctly so that no coefficient corrections appear and the missing interaction is right from the very beginning, with no extra harmful terms. This approach may be called "Reformulation".

I chose simple mechanical equations on purpose to demonstrate unambiguously what is going on in QFT in reality. My model can be reformulated (=renormalized) exactly and perturbatively. I would like to see your opinions whether it is comprehensible and convincing or not.

**Further explanation**

There goes a discussion about what we should allow to the review section. My "reformulation" direction is called there a bullshit by dimension10.

Let me say a word in my defence. There is a formulation (a mainstream one) where the Lagrangian $L_{phys}$ only contains physical constants, but there is also a counter-term Lagrangian $L_{CT}$ next to it $L_{full}=L_{phys}+L_{CT}$. Conter-terms are supposed to subtract undesirable corrections "generated" with the original interaction Lagrangian $L_{int}$ containing in $L_{phys}$. Normally, the counter-term Lagrangian is joined with the interaction Lagrangian in one "renormalized" interaction and they are treated perturbatively. Subtractions are fulfilled in each order of perturbation theory starting from loop-like diagrams.

What if we could make the subtractions in the full Lagrangian exactly, before building the perturbation theory? Then we would not have to do any subtractions in our calculations. The perturbation theory would be different - with no harmful corrections to the equation coefficients, it would be just a regular, rootine calculation.

Currently we cannot carry out such subtractions in the full Lagrangian, unfortunately. So we do it perturbatively. In my toy model, however, it is possible. After that we arrive at a new expression of Lagrangian $L_{full}$ yielding a regular perturbation theory. In other words, reformulation is an exact renormalization of the full Lagrangian and it gives the same results, but directly. So it is not a bullshit, but a shortcut to the right results.

By the way, this new (exactly renormalized) Lagrangian contains a slightly different, but quite understandable and acceptable physics. That is why I believe that we physicists can figure out a realistic right Lagrangian from the physical reasonings.

Please, do not vote down this message. I already lost the right to vote answers up. Otherwise, I will quit your noble academy here.