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1
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84926789321
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For reviews, see (a) S. R. de Groot and L. G. Suttorp, Foundations of Electrodynamics (North-Holland, Amsterdam, 1972), Appendix to Chap. VI;
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13
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84926811353
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The Liouville space bra-ket notation is found, e.g., in (a), in Proble`me a` N Corps, 1967 Les Houches Lectures, edited by C. De Witt and, (Gordon and Breach, London, 1968), and is used extensively in spectroscopy, where it was introduced by (b) A. Ben-Reuven
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(1966)
Phys. Rev.
, vol.141
, pp. 34
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des Cloiseaux, J.1
Balian, R.2
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20
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84926855264
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H. Weyl, The Theory of Groups and Quantum Mechanics (Dover, New York, 1950), pp. 272 – 276.
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21
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P. A. M. Dirac, The Principles of Quantum Mechanics, 4th ed. (Oxford University Press, New York, 1958), pp. 83 – 89.
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22
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84926855263
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For example, Dirac [who denotes the position operator by q and positions (numbers) by q prime] lets | PSI (q) rangle be the ket whose projection on langle q prime | is PSI ( q prime ). Our partial / partial (q hat ) is denoted d / d q by Dirac.
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25
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84926855262
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F. R. Gantmacher, The Theory of Matrices (Chelsea, New York, 1960), Vol. 1, Chap. VIII.
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26
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84926811351
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Note that (6.5) alone, without Galilean invariance, does not necessarily imply (6.4) mdashone could have τ hat hat | u ; φ rcurl = ei γ | τ u ; φ rcurl where the phase gamma may depend on tau and u.
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27
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4244198097
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discussed this canonical set of superoperators, but without relating it to the Wigner-Weyl formulation.
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(1979)
Physica A
, vol.99
, pp. 369
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George, C.1
Prigogine, I.2
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34
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84926811350
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R. P. Feynman, in Quantum Implications, Essays in Honour of David Bohm, edited by B. J. Hiley and F. D. Peat (Routledge and Kegan Paul, New York, 1987); see also Ref. 15.
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37
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84926855260
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This may be seen by proceeding as in Eq. (2.15), using (7.1) instead of (2.6).
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38
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84926855259
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F. Bopp, in Werner Heisenberg und die Physik unserer Zeit (Vieweg, Braunschweig, 1961), p. 128;
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40
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(a) I. Prigogine, Non-Equilibrium Statistical Mechanics (Wiley, New York, 1962);
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43
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(b) A. Royer, in The Physics of Phase Space, edited by Y. S. Kim and W. W. Zachary (Springer, New York, 1987);
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