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Articles by Felix M. Lev
On the Basics of Mathematics
Submitted: 28 September 2025 Posted: 29 September 2025 You are already at the latest version As shown in the works of Gödel and others, standard mathematics has foundational problems because it invokes the infinite ring of integers Z. At the same time, finite mathematics proceeds from a finite ring Rp=(0,1,2,...p-1) of residues modulo p. We give a new and simple proof that Z is the limit of Rp when \( p\to\infty \). The proof involves only potential infinity and not actual infinity.
Why Poincare Symmetry Is a Good Approximate Symmetry in Particle Theory
1. Problem Statement In quantum field theory (QFT), relativistic (Poincare) symmetry is explained as follows. The Poincare group is the group of motions of Minkowski space, and the quantum system under consideration (which, in the general case, can consist of an arbitrary number of interacting elementary particles) should be described by unitary representations of this group.
Main Problems in Constructing Quantum Theory Based on Finite Mathematics
This is an early access version, the complete PDF, HTML, and XML versions will be available soon. Open AccessReview by Felix M.
Finite Mathematics as the Most General (Fundamental) Mathematics
1. The Main Goal of This Paper In [1,2] and other our publications, we investigated in detail why finite mathematics based on a finite ring of characteristic p is more general (fundamental) than standard mathematics. These publications contain detailed proofs of statements on which our approach is based. The purpose of this paper is to explain the main ideas of our approach at the simplest possible level.
Solving Particle-Antiparticle and Cosmological Constant Problems
1. General Principles of Quantum Theory In this paper we solve the particle-antiparticle and cosmological constant problems proceeding from quantum theory, which postulates: ( H ) Various states of the system under consideration are elements of a Hilbert space H with a positive definite metric, that is, the norm of any non-zero element of H is positive. ( O ) Each physical quantity is defined by a self-adjoint operator O in H .
Mark Burgin’s Contribution to the Foundation of Mathematics
1. Problems in the Foundation of Classical Mathematics The title of the famous Wigner paper [1] is: “The unreasonable effectiveness of mathematics in the natural sciences”, and the paper concludes as follows: “The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve.
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