Finite Mathematics as the Foundation of Classical Mathematics and Quantum Theory

1. Front Matter

   Pages i-xvii

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2. Introduction

   • Felix Lev

   Pages 1-32

3. A New Look at the Position Operator in Quantum Theory

   • Felix Lev

   Pages 33-95

4. Basic Properties of dS Quantum Theories

   • Felix Lev

   Pages 97-123

5. Algebraic Description of Irreducible Representations

   • Felix Lev

   Pages 125-138

6. Two-Body Systems in Discrete Basis

   • Felix Lev

   Pages 139-167

7. Why Finite Mathematics Is the Most General and Finite Quantum Theory Is More Pertinent Physical Theory Than Standard One

   • Felix Lev

   Pages 169-194

8. Semiclassical States in Modular Representations

   • Felix Lev

   Pages 195-200

9. Basic Properties of AdS Quantum Theories

   • Felix Lev

   Pages 201-234

10. Dirac Singletons As the Only True Elementary Particles

    • Felix Lev

    Pages 235-250

11. A Conjecture on the Nature of Time

    • Felix Lev

    Pages 251-260

12. Discussion and Conclusion

    • Felix Lev

    Pages 261-283

13. Back Matter

    Pages 285-291

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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.

• Finite Quantum theory
• Foundation of Quantum Theory
• Quantum de Sitter Symmetry
• Foundation of Mathematics
• Gravity in Finite Quantum Theory
• Cosmological Accelleration and de Sitter Symmetry
• Particle and Antiparticle Quantum Numbers
• Quantal Paradox for Photons from Stars
• Dirac Singletons
• Nature of Time Conjecture

• Torrance, USA

  Felix Lev

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.

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