Популярно о конечной математике и ее интересных применениях в квантовой теории

I cannot recommend publication of this paper due to the following reasons:

Essentially, the results discussed in the paper are not new, being largely based on previously published work by the same author, e.g. Ref. [9]. The paper does not address the cosmological constant problem, neither it shows convincingly that “the problem does not arise”, as claimed in the abstract. Therefore, this work does not lead to any significant advance of our understanding of dark energy, and for this reason I can hardly see how it would be of interest to the Journal’s readership.

Section 2 is a naive, incomplete and unnecessarily lengthy discussion of the subject of limiting theories, based on two examples: Newtonian mechanics as a limiting case of special relativity, and the classical limit of quantum mechanics. The related notions of physical dimensions and units of measurement are systematically confused throughout the paper (I recommend https://arxiv.org/abs/physics/0110060 for a clear discussion of the subject).

The Author claims that deSitter and Anti-deSitter spacetimes are more “fundamental” than Minkowski spacetime, since the latter can be obtained as a particular case when the cosmological constant (or, equivalently, the curvature radius) is sent to zero. However, this only shows that dS and AdS spacetime are more general than Minkowski. Neither the former are more symmetric than the latter, as claimed on page 6 (all of them are maximally symmetric spacetimes). It is simply incorrect to speak of a given spacetime geometry as being more fundamental than another; rather, the attribute “fundamental” should be used with reference to a dynamical theory having a broader regime of applicability compared to a particular limit. Moreover, neither the value nor the sign of the cosmological constant can be fixed following the arguments in the paper.

Without a theory (as given by, e.g., an action principle), there is no reason to assume a particular spacetime geometry (e.g. deSitter) as being a valid description for the vacuum. Moreover, it is quite challenging to build a theory of gravity where the cosmological constant (or, equivalently, the deSitter radius) matches the observed value without introducing new tunable parameters: finding such a theory could in fact be regarded as a solution of the cosmological constant problem. Such a crucial aspect is not discussed at all in the paper, and the Author does not propose any theory to frame his discussion.