Does renormalization means discarding corrections to a known constant?

In summary, Renormalization in QED involves replacing the original Hamiltonian with a new one that includes additional counterterms to cancel infinite contributions from self-interactions of particles. This process leads to finite and accurate scattering amplitudes, but the reason for its success is still unknown. The question remains whether renormalization is equivalent to discarding corrections to known constants, and this is an ongoing debate among experts.
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The article "On Perturbation Theory for the Sturm-Liouville Problem with Variable Coefficients" by Vladimir Kalitvianski is available at http://arxiv.org/abs/0906.3504.

Here I show how one can reformulate the original problem in order to eliminate big (or divergent) perturbative corrections and obtain finite series from the very beginning.
 

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