Популярно о конечной математике и ее интересных применениях в квантовой теории

The manuscript written by Dr. Felix M. Lev deals with an approach to quantum mechanics and quantum field theory based on a finite field or ring. Focus is on the role of time (and space), space-time symmetries (from Poincare to dS and AdS) and IRs thereof, the semiclassical approximation and (some) classical results, obtained without making explicit reference to the standard semiclassical limit. Let me add that I have some basic knowledge in finite mathematics (enough knowledge to appreciate the content of Sec. 5). I wonder whether Dr. Lev is correct when he asserts that this knowledge is not shared by the majority of physicists. He is certainly a bit superficial when he writes that “referees in physics community [very often] do not have even very basic knowledge in the problem discussed in the refereed paper." This is certainly not true for Physical Review A.

But let me come to the point. I quote from the APS webpage: Physical Review A publishes important developments in the rapidly evolving areas of atomic, molecular, and optical (AMO) physics, quantum information, and related fundamental concepts. (I wrote “related" in italics.) There is one section on “Fundamental concepts" that covers what used to be considered (in the period that followed the discovery of Bell's theorem) foundational issues in the interpretations of quantum mechanics. Such an area of research has recently evolved into a very active field of investigation, dealing with entanglement, other quantum correlations, dissipative quantum systems and evolutions, quantum maps, quantum applications and also quantum technologies (this list is far from being exhaustive). In his accompanying letters, Dr. Lev wrote that “Your journal has a section “Fundamental Concepts" and my paper satisfies all the requirements for that section." In my opinion there is a misunderstanding. This expression has a different connotation. I quote again the webpage of Physical Review A: PRA covers atomic, molecular, and optical physics, foundations of quantum mechanics, and quantum information, including:

Fundamental concepts

Quantum information

Atomic and molecular structure and dynamics

Atomic and molecular collisions and interactions

Atomic and molecular processes in external fields, including interactions with strong fields and short pulses

Matter waves and collective properties of cold atoms and molecules

Quantum optics, physics of lasers, nonlinear optics, and classical optics

The ideas investigated in this manuscript are of interest, but do not appear to be in line with the scope of Physical Review A, for the reasons I have detailed. I believe that Physical Review A is not the right arena to discuss the issues brought up by Dr. Lev. I therefore suggest that this manuscript be submitted to a different journal, where appropriate refereeing can be provided.

In conclusion, I uphold the rejection of the Associate Editor Marek Zukowski and do not recommend publication in Physical Review A.