Book contents
- Frontmatter
- Contents
- Preface
- Part I Discrete time concepts
- Part II Classical discrete time mechanics
- 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
- Part III Discrete time quantum mechanics
- Part IV Discrete time classical field theory
- Part V Discrete time quantum field theory
- Part VI Further developments
- Appendix A Coherent states
- Appendix B The time-dependent oscillator
- Appendix C Quaternions
- Appendix D Quantum registers
- References
- Index
15 - Intermission
from Part II - Classical discrete time mechanics
Published online by Cambridge University Press: 05 May 2014
- Frontmatter
- Contents
- Preface
- Part I Discrete time concepts
- Part II Classical discrete time mechanics
- 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
- Part III Discrete time quantum mechanics
- Part IV Discrete time classical field theory
- Part V Discrete time quantum field theory
- Part VI Further developments
- Appendix A Coherent states
- Appendix B The time-dependent oscillator
- Appendix C Quaternions
- Appendix D Quantum registers
- References
- Index
Summary
This chapter forms a natural divide half-way into the book. In the first half, we discussed the principles of discrete time (DT) classical mechanics (CM). In the second half we focus mainly on quantum principles. This chapter is a good place in which to take stock of what we have done, what we plan to do, and how the two halves of the book are related. The common theme is Lee's approach to DT mechanics, discussed in Chapter 10.
As we implied previously, theorists whose work is relevant to us can be classified into two types: the applied mathematicians and the mathematical physicists, who may also be called fundamentalists. This division is based not on any value judgements but on the motivations and ambitions driving a theorist's work, which are generally easy to identify.
The applied mathematicians fall into two categories. The first consists of those interested in finding better ways of understanding CM and, if necessary, finding ever better approximations to it. They explore DT CM with that in mind and are generally not remotely interested in quantum mechanics (QM). The second category consists of quantum theorists, such as Bender, who develop DT numerical simulation to approximate standard QM. Lattice gauge theorists also fall into the applied group, since their discretization of spacetime is regarded at all times as an approximation to the continuum.
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- Information
- Principles of Discrete Time Mechanics , pp. 170 - 178Publisher: Cambridge University PressPrint publication year: 2014