Finite Mathematics as the Foundation of Classical Mathematics and Quantum Theory

lt;b>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.

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