×

zbMATH — the first resource for mathematics

Superpositions of states and a representation theorem. (English) Zbl 0453.03066

MSC:
03G12 Quantum logic
81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
81P20 Stochastic mechanics (including stochastic electrodynamics)
46C99 Inner product spaces and their generalizations, Hilbert spaces
46E27 Spaces of measures
PDF BibTeX XML Cite
Full Text: Numdam EuDML
References:
[1] R. Baer , Linear algebra and projective geometry , Academic Press , New York , 1952 (Russian translation IL, Moscow , 1955 ). MR 52795 | Zbl 0049.38103 · Zbl 0049.38103
[2] E.G. Beltrametti and G. Cassinelli , Logical and mathematical structures of quantum mechanics , Riv. Nuovo Cim. , vol. 6 , 1976 , p. 321 - 404 . MR 438918 · Zbl 0365.06002
[3] G. Birkhoff , Lattice theory , Amer. Math. Soc. , Coll. Publ. , New York , 1967 . Zbl 0153.02501 · Zbl 0153.02501
[4] S.P. Gudder , Uniqueness and existence properties of bounded observables , Pacific. J. Math. , vol. 19 , 1966 , p. 81 - 93 . Article | MR 201146 | Zbl 0149.23603 · Zbl 0149.23603
[5] S.P. Gudder , A superposition principle in physics , J. Math. Phys. , vol. 11 , 1970 , p. 1037 - 1040 . MR 261868 | Zbl 0191.26901 · Zbl 0191.26901
[6] S.P. Gudder , Projective representations of quantum logics , Int. J. Theoret. Phys. , vol. 3 , 1970 , p. 99 - 108 . MR 416297
[7] W. Guz , On the lattice structure of quantum logics , Ann. Inst. Henri Poincaré , vol. 28 , 1978 , p. 1 - 7 . Numdam | MR 495046
[8] F. Maeda and S. Maeda , Theory of symmetric lattices , Springer-Verlag , Berlin , 1970 . MR 282889 | Zbl 0219.06002 · Zbl 0219.06002
[9] S. Pulmannova , A superposition principle in quantum logics , Commun. Math. Phys. , vol. 49 , 1976 , p. 47 - 51 . Article | MR 431978
[10] S. Pulmannova , The superposition principle and sectors in quantum logics , Int. J. Theoret. Phys. , to be published. Zbl 0491.03022 · Zbl 0491.03022
[11] V.S. Varadarajan , Probability in physics and a theorem on simultaneous observability , Commun. Pure Appl. Math. , vol. 15 , 1962 , p. 189 - 217 . MR 163616 | Zbl 0109.44705 · Zbl 0109.44705
[12] V.S. Varadarajan , Geometry of quantum theory , Van Nostrand , Princeton , N. Y ., 1968 . MR 471674 | Zbl 0155.56802 · Zbl 0155.56802
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.