Principles of discrete time mechanics

Author(s)

• Jaroszkiewicz, George

Bibliographic Information

Principles of discrete time mechanics

George Jaroszkiewicz

（Cambridge monographs on mathematical physics）

Cambridge University Press, 2014

Note

Includes bibliographical references and index

Contents of Works

• The physics of discreteness
• The road to calculus
• Temporal discretization
• Discrete time dynamics architecture
• Some models
• Classical cellular automata
• The action sum
• Worked examples
• Lee's approach to discrete time mechanics
• Elliptic billiards
• The construction of system functions
• The classical discrete time oscillator
• Type 2 temporal discretization
• Discrete time quantum mechanics
• The quantized discrete time oscillator
• Path integrals
• Quantum encoding
• Discrete time classical field equations
• The discrete time Schrodinger equation
• The discrete time Klein-Gordon equation
• The discrete time Dirac equation
• Discrete time Maxwell's equations
• The discrete time Skyrme model
• Discrete time quantum field theory
• Interacting discrete time scalar fields
• Space, time and gravitation
• Causality and observation
• Concluding remarks

Description and Table of Contents

Description

Could time be discrete on some unimaginably small scale? Exploring the idea in depth, this unique introduction to discrete time mechanics systematically builds the theory up from scratch, 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, including spreadsheet mechanics, classical and quantum register mechanics, and classical and quantum mechanics and field theories. A consistent emphasis on contextuality and the observer-system relationship is maintained throughout.

Table of Contents

• 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.

by "Nielsen BookData"

Details

• NCID: BB15676263
• ISBN:
  • 9781107034297
• LCCN: 2013039555
• Country Code: uk
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Cambridge
• Pages/Volumes: xiv, 365p.
• Size: 26 cm
• Classification:
  • LCC : QC174.13
  • DC23 : 530.12
• Subject Headings:
  • LCSH : Quantum theory -- Mathematics
  • LCSH : Mechanics
• Parent Bibliography ID:
  • BA00074521