Finite Mathematics as the Foundation of Classical Mathematics and Quantum Theory

With Applications to Gravity and Particle Theory
1. Auflage 2020
ISBN: 978-3-030-61100-2
Verlag: Springer International Publishing

Buch, Englisch, 291 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 635 g

This book delves into finite mathematics and its application in physics, particularly quantum theory. It is shown that quantum theory based on finite mathematics is more general than standard quantum theory, whilst finite mathematics is itself more general than standard mathematics.As a consequence, the mathematics describing nature at the most fundamental level involves only a finite number of numbers while the notions of limit, infinite/infinitesimal and continuity are needed only in calculations that describe nature approximately. It is also shown that the concepts of particle and antiparticle are likewise approximate notions, valid only in special situations, and that the electric charge and baryon- and lepton quantum numbers can be only approximately conserved.

Zielgruppe

Research

Autoren/Hrsg.

Lev, Felix

Fachgebiete

• Naturwissenschaften Physik Quantenphysik Kernphysik
• Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik
• Naturwissenschaften Physik Quantenphysik Relativität, Gravitation
• Naturwissenschaften Physik Physik Allgemein Geschichte der Physik

Inhaltsverzeichnis

Introduction.- A new look at the position operator in quantum theory.- Basic properties of de Sitter quantum theories.- Algebraic description of irreducible representations.- Two-body systems in discrete basis.- Why finite mathematics is the most general and finite quantum theory is more pertinent physical theory than standard one.- Semiclassical states in modular representations.- Basic properties of anti-de Sitter quantum theories.- Dirac singletons as the only true elementary particles.- A conjecture on the nature of time 11. Discussion and conclusion

Über Autor(innen)

Felix Lev received Master’s degree from the Moscow Institute for Physics and Technology (Moscow, Russia), Ph.D. from the Institute of Theoretical and Experimental Physics (Moscow, Russia) and Dr. Sci. degree from the Institute for High Energy Physics (Serpukhov Accelerator) (Protvino, Russia). He was Leading Scientist of the Joint Institute for Nuclear Research (Dubna, Russia) and currently he is Senior scientist of Artwork Conversion Software Inc (Manhattan Beach, California, USA). He is the author of more than 100 publications in leading journals on physics and mathematical physics.