Finite Mathematics as the Foundation of Classical Mathematics and Quantum Theory : With Applications to Gravity and Particle Theory

Lev, Felix

Springer Nature Switzerland AG（2020/11発売）

• 製本 Hardcover:ハードカバー版／ページ数 291 p.
• 言語 ENG
• 商品コード 9783030611002

Full Description

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.

Contents

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