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Operational quantum physics. (English) Zbl 0863.60106
Lecture Notes in Physics. New Series m: Monographs. m31. Berlin: Springer-Verlag. xi, 230 p. (1995).
A systematic discussion of the fundamental aspects of quantum theory and of related recent experiments are presented in terms of POV (positive operator valued) measure for observables (instead of the standard projection valued measure), where a POV measure is an assignment of a positive operator to each measurable set, satisfying sigma-additivity and normalization (i.e. the identity operator is assigned to the total space). The first two chapters provide the motivations behind and a systematic development of the physical concepts and mathematical languages, including foundations for measurement theory and operational interpretation. Chapter 3 illustrates the use of POV measures in carrying out the covariance point of view for the operational definition of observables where the underlying space-time symmetry is that of the Galilei group. The foundation of quantum mechanics is addressed in Chapters 4-6. For example, a realistic interpretation of quantum mechanics as a theory for individual systems introduced in the first two chapters is illustrated in the phase space measurement model of Chapter 6, where Heisenberg’s interpretation of the indeterminacy relation in terms of individual, irreducible quantum inaccuracies is demonstrated. Experimental examples are provided in Chapter 7.
Reviewer: H.Araki (Tokyo)

60K40 Other physical applications of random processes
81-02 Research exposition (monographs, survey articles) pertaining to quantum theory
60-02 Research exposition (monographs, survey articles) pertaining to probability theory
Full Text: DOI
[1] Pauli, W.: General principles of quantum theory. (1980) · Zbl 0439.34044
[2] Busch, P.: Found. phys.. 20, 1 (1990)
[3] Dirac, P. A. M.: Proc. R. Soc. A. 114, 243 (1927)
[4] Ludwig, G.: Foundations of quantum mechanics. 1 (1983) · Zbl 0509.46057
[5] Holevo, A. S.: Probabilistic and statistical aspects of quantum theory. (1982) · Zbl 0497.46053
[6] Srinivas, M. D.; Vijayalakshmi, R.: Pramana. 16, 173 (1981)
[7] Werner, R.: J. math. Phys.. 27, 793 (1986)
[8] Aharonov, Y.; Bohm, D.: Phys. rev.. 122, 1649 (1961)
[9] Busch, P.; Grabowski, M.; Lahti, P.: Who is afraid of POV measures? unified approach to quantum phase observables. (1994)
[10] Garrison, J. C.; Wong, J.: J. math. Phys.. 11, 2242 (1970)
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