The elements of continuum mechanics by Clifford A. Truesdell

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By Clifford A. Truesdell

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3) to hold, just as for other canonically conjugate pairs of operators such as position and momentum, which satisfy the standard commutation relation [ˆ p, x ˆ] = −i . A heuristic proof of Pauli’s theorem goes as follows. In standard QM, conjugate pairs of operators can be interpreted as generators of canonically conjugate transformations. 4) whilst the momentum operator pˆ generates translations in space according to the rule exp(iaˆ p/ )|x = |x − a . 3). 6) which should hold for all real values of ε.

Part III, Discrete time quantum mechanics, consists of Chapters 16 to 19 and discusses quantization principles relevant to DT mechanics. Part IV, Discrete time classical field theory, consists of Chapters 20 to 25 and extends the quantization principles discussed in Part III to scalar, Dirac and Maxwell fields. Emphasis is placed on DT gauge invariance. Part V, Discrete time quantum field theory, consists of Chapters 26 and 27 and deals with second quantization of the fields discussed in the previous section.

Part VI, Further developments, runs from Chapter 28 to Chapter 30. This part discusses DT concepts associated with spacetime and concludes the book. Appendices are included in order to review some relevant topics such as coherent states, time-dependent oscillators and quantum registers. 1 The natural occurrence of discreteness Although the conventional experience of time gives a strong impression that time ‘flows’ in a continuous way, humans have always measured time in discrete units such as hours, days, months and years.

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