Algebra of observables and quantum logic
Annales de l'institut Henri Poincaré. Section A, Physique Théorique, Tome 19 (1973) no. 4, pp. 297-331. 
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     author = {Cirelli, Renzo and Gallone, Franco},
     title = {Algebra of observables and quantum logic},
     journal = {Annales de l'institut Henri Poincar\'e. Section A, Physique Th\'eorique},
     pages = {297--331},
     publisher = {Gauthier-Villars},
     volume = {19},
     number = {4},
     year = {1973},
     mrnumber = {373491},
     zbl = {0294.46050},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1973__19_4_297_0/}
}
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Cirelli, Renzo; Gallone, Franco. Algebra of observables and quantum logic. Annales de l'institut Henri Poincaré. Section A, Physique Théorique, Tome 19 (1973) no. 4, pp. 297-331. http://www.numdam.org/item/AIHPA_1973__19_4_297_0/

[1] I.E. Segal, Ann. Math., t. 48, 1947, p. 930. | MR | Zbl

[2] J.M. Jauch, Helv. Phys. Acta, t. 33, 1960, p. 711 ; J.M. Jauch and B. Misra, Ibid., t. 34, 1961, p. 699. | MR | Zbl

[3] V.S. Varadarajan, Geometry of Quantum Theory, vol. I, Princeton, 1968. | MR | Zbl

[4] G. Ludwig, Z. Phys., t. 181, 1964, p. 233. | MR | Zbl

[5] E. Chen, J. Math. Phys., t. 12, 1971, p. 2364. | MR | Zbl

[6] M. Guenin, J. Math. Phys., t. 7, 1966, p. 271. | MR | Zbl

[7] C. Piron, Helv. Phys. Acta, t. 42, 1969, p. 330. | MR | Zbl

[8] J. Dixmier, Les algèbres d'opérateurs dans l'espace hilbertien (Algèbres de von Neumann), Paris, 1957 (première édition); 1969 (deuxième édition). | Zbl

[9] K. Maurin, General Eigenfunction Expansions and Unitary Representations of Topological Groups, Warszawa, 1968. | MR | Zbl

[10] J.-P. Eckmann et M. Guenin, Méthodes Algébriques en Mécanique Statistique, Berlin, 1969; R. Giles, J. Math. Phys., t. 11, 1970, p. 2139. | MR | Zbl

[11] A.M. Gleason, J. Rat. Mech. Anal., t. 6, 1957, p. 885. | Zbl

[12] G.C. Wick, A.S. Wightman and E.P. Wigner, Phys. Rev., t. 88,1952, p. 101. | MR | Zbl

[13] P.A.M. Dirac, The Principles of Quantum Mechanics, 4th ed., Oxford, 1958. | Zbl

[14] G.G. Emch, Rigourous Results in Non-Equilibrium Statistical Mechanics (Lectures in Theoretical Physics, VIII a, Boulder, 1966). | MR

[15] J. Dixmier, Les C*-algèbres et leurs représentations, 2.5.5, Paris, 1964. | MR | Zbl

[16] J.M. Jauch, Foundations of Quantum Mechanics, Reading, Massachusetts, 1968. | MR | Zbl

[17] S.P. Gudder, J. Math. Phys., t. 11, 1970, p. 1037. | Zbl

[18] F. Gallone and A. Mania, Ann. Inst. H. Poincaré, t. 15 A, 1971, p. 37. | Numdam | MR | Zbl

[19] C. Piron, Helv. Phys. Acta, t. 37, 1964, p. 439; Jauch's book quoted in ref. [16] ; J.M. Jauch and C. Piron, Ibid., t. 42, 1969, p. 842. | MR | Zbl

[20] C. Piron, Helv. Phys. Acta, t. 37, 1964, p. 439; I. Amemiya and H. Araki, Publ. Research Inst. Math. Kyoto University, t. A2, 1967, p. 423. | MR

[21] C. Piron, Lecture Notes of Varenna Summer School, 1970.

[22] S. Gudder and C. Piron, J. Math. Phys., t. 12, 1971, p. 1583; R. Cirelli and P. Cottaramusino, On the isomorphism of a « quantum logic » with the logic of the projections in a Hilbert space, Preprint IFU M 135/FT, University of Milano.

[23] E.C.G. Stueckelberg, Helv. Phys. Acta, t. 33, 1960, p. 727; G. Emch, Ibid., t. 36, 1963, p. 739, p. 770. | MR

[24] V.I. Smirnov, A Course of higher mathematics, vol. V, § 192, Oxford, 1964.