Covering classical and quantum discrete time mechanics, this book presents all the tools needed to formulate and develop applications of discrete time mechanics in a number of areas, beginning with the historical, physical and mathematical background to the chronon hypothesis.
Covering classical and quantum discrete time mechanics, this book presents all the tools needed to formulate and develop applications of discrete time mechanics in a number of areas, beginning with the historical, physical and mathematical background to the chronon hypothesis.
George Jaroszkiewicz is an Associate Professor at the School of Mathematical Sciences, University of Nottingham, having formerly held positions at the University of Oxford and the University of Kent.
Inhaltsangabe
1. Introduction 2. The physics of discreteness 3. The road to calculus 4. Temporal discretization 5. Discrete time dynamics architecture 6. Some models 7. Classical cellular automata 8. The action sum 9. Worked examples 10. Lee's approach to discrete time mechanics 11. Elliptic billiards 12. The construction of system functions 13. The classical discrete time oscillator 14. Type 2 temporal discretization 15. Intermission 16. Discrete time quantum mechanics 17. The quantized discrete time oscillator 18. Path integrals 19. Quantum encoding 20. Discrete time classical field equations 21. The discrete time Schrodinger equation 22. The discrete time Klein¿Gordon equation 23. The discrete time Dirac equation 24. Discrete time Maxwell's equations 25. The discrete time Skyrme model 26. Discrete time quantum field theory 27. Interacting discrete time scalar fields 28. Space, time and gravitation 29. Causality and observation 30. Concluding remarks Appendix A. Coherent states Appendix B. The time-dependent oscillator Appendix C. Quaternions Appendix D. Quantum registers References Index.
1. Introduction 2. The physics of discreteness 3. The road to calculus 4. Temporal discretization 5. Discrete time dynamics architecture 6. Some models 7. Classical cellular automata 8. The action sum 9. Worked examples 10. Lee's approach to discrete time mechanics 11. Elliptic billiards 12. The construction of system functions 13. The classical discrete time oscillator 14. Type 2 temporal discretization 15. Intermission 16. Discrete time quantum mechanics 17. The quantized discrete time oscillator 18. Path integrals 19. Quantum encoding 20. Discrete time classical field equations 21. The discrete time Schrodinger equation 22. The discrete time Klein¿Gordon equation 23. The discrete time Dirac equation 24. Discrete time Maxwell's equations 25. The discrete time Skyrme model 26. Discrete time quantum field theory 27. Interacting discrete time scalar fields 28. Space, time and gravitation 29. Causality and observation 30. Concluding remarks Appendix A. Coherent states Appendix B. The time-dependent oscillator Appendix C. Quaternions Appendix D. Quantum registers References Index.
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