Abstract
We briefly review general concepts of renormalization in quantum field theory and discuss their application to solutions of integral equations with singular potentials in the few-nucleon sector of the low-energy effective field theory of QCD. We also describe a particular subtractive renormalization scheme and consider a specific application to a toy-model with a singular potential serving as its effective field theoretical leading-order approximation.
Highlights
In this paper we discussed the problem of renormalization of singular potentials in the low-energy effective field theory of the strong interactions
We outlined the standard procedure of quantum field theoretical renormalization emphasizing its general definition that applies to both non-perturbative as well as perturbative calculations
The main message of our work is that chiral effective field theory (EFT) in the few-nucleon sector does not require the invention of any new non-perturbative renormalization that would go beyond what is already well-established in quantum field theory
Summary
It is well known how to renormalize Feynman diagrams in quantum field theories. it turns out to be a chalenging problem to properly renormalize the non-perturbative solutions to integral equations since this usually requires taking into account contributions of an infinite number of counter terms. Reading the literature in the few-body sector of lowenergy chiral EFT and references therein, one often gets the impression that there is no well-established concept of renormalization for non-perturbative problems in quantum field theories, and that we are currently seeking for such a self-consistent definition. In this quest for the solution of a technically challenging problem, fundamental concepts that are well established and should be well-known to the practitioners are often ignored or even disputed in the nuclear physics community.
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