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Principles of Discrete Time Mechanics

$134.00 (C)

Part of Cambridge Monographs on Mathematical Physics

  • Date Published: June 2014
  • availability: Available
  • format: Hardback
  • isbn: 9781107034297

$ 134.00 (C)
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  • 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.

    • Demonstrates the feasibility of discrete time mechanics, and intended to stimulate further developments in this approach to physics
    • Includes an accessible exploration of spreadsheet mechanics, allowing exploration of a limitless variety of cellular dynamical models, giving insight into relativistic lightcones and time dilation
    • Written such that the discrete time hypothesis is the only new concept readers need to take on board: all other familiar concepts are retained
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    Product details

    • Date Published: June 2014
    • format: Hardback
    • isbn: 9781107034297
    • length: 360 pages
    • dimensions: 254 x 180 x 30 mm
    • weight: 0.86kg
    • contains: 21 b/w illus.
    • availability: Available
  • 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.

  • Author

    George Jaroszkiewicz, University of Nottingham
    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.

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