Популярно о конечной математике и ее интересных применениях в квантовой теории

The rejection of my paper was based on the Associate Editor’s comment consisting of one sentence: “This paper does not present an important result in mathematical physics.” This comment, given without any explanation, indicates that the Associate Editor did not carefully read the paper and/or was unable to understand its results. The fact that the paper contains fundamental new results in mathematical physics has been explained in the cover letter and in the paper itself. However, in view of the comment, I will try to briefly explain this point again.

The concept of particle-antiparticle is a fundamental concept of mathematical physics and particle physics. This concept is considered in detail in my book recently published by Springer: Felix Lev, Finite Mathematics as the Foundation of Classical Mathematics and Quantum Theory. With Application to Gravity and Particle theory. ISBN 978–3–030–61101–9. Springer, https://www.springer.com/us/book/9783030611002. Here it is explained that the concept has a physical meaning only in very special cases when the symmetry algebra is such that its irreducible representations (IRs) contain states with either only positive or only negative energies, i.e., the IRs cannot contain states with both signs of energies. For algebras important for particle physics this takes place only for IRs of the Poincare and anti-de Sitter Lie algebras over complex numbers. Those algebras are special degenerate cases of more general algebras for which IRs contain states with both signs of energies, and therefore for such algebras the concept of particle-antiparticle does not have a physical meaning. At the present stage of the universe the Poincare symmetry works with a very high accuracy and that is why at this stage the concept of particle-antiparticle also is valid with a very high accuracy. However, at very early stages of the universe the symmetry algebras cannot be such that the concept of particle-antiparticle has a physical meaning. This immediately explains that the known problem of the baryon asymmetry of the universe (BAU) does not arise. The explicit consideration of relevant IRs requires lengthy calculations, and they were described in the book and in my papers published in known journals (in particular, in my two rather long papers in JMP). But the BAU problem has been mentioned in the book very briefly. On the contrary, in the given paper (which is rather short) I explain only the meaning of the results on IRs with references to the book, and then explain how the results on IRs are applied to the BAU problem.

When Professor Solovej became the Editor in Chief of JMP, he wrote in his introductory note that “…It should publish high-quality papers of interest to both mathematics and physics, and this criterion should be applied vigorously in the review of papers. …We should put quality before quantity.” I believe that my paper fully satisfies these requirements because it considers not only mathematical results of constructing different IRs but also shows how those results are applied to the known physical problem. I believe that for quantum physicists it should be obvious that the concept of particle-antiparticle is fundamental, my approach to this concept is fully new, the BAU problem is fundamental, and my approach to this problem also is new. So, I believe that my paper should be published or not depending only on whether my results are correct or not. So, when the Associate Editor writes that “This paper does not present an important result in mathematical physics” then this sentence can be treated as a scientific conclusion only if he/she explicitly explains why he/she treats my results as non-important. I think it is obvious that when the author sends a paper to JMP, he/she is interested not only in whether the paper will be published or not but also in knowing the opinion of qualified physicists/mathematicians. However, my previous paper also has been rejected with only one sentence: “The paper is not of sufficient mathematical quality to warrant publication in Journal of Mathematical Physics.” and without any explanation. This poses a question whether JMP understands that official negative statements without any explanation contradict scientific ethics.

When I wrote an appeal on the first rejection, Professor Solovej responded: “It is certainly not enough that the statements are correct. Your paper seems better suited for a journal addressing fundamental issues of physics.” I was surprised that JMP does not consider papers “addressing fundamental issues of physics”. But maybe, my paper was treated as only a mathematical one? In any case, the present paper fully satisfies Professor Solovej’s criteria because it shows how mathematics is applied to a fundamental problem of physics. I would be grateful if the editorial decision on my paper is reconsidered. I still hope that JMP has highly qualified physicists and mathematicians who can judge my paper on the basis of scientific criteria.