Abstract
This contribution continues the series of papers [2, 4, 5, 12] treated by Ludwig and collaborators. It is based on the generalized frame given in [6]; there Ludwig has set up an “infinite” axiomatic scheme as extension of the “finite” system [4, 5]. The results of [12] are then proved for a “locally finite” case; they lead to an extended representation theorem.
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References
Amemiya, I., Araki, H.: A remark on Piron's paper. Publ. res. Inst. math. Sci., Kyoto Univ., Ser.A 2, 423–427 (1966).
Dähn, G.: Attempt of an axiomatic foundation of quantum mechanics and more general theories IV. Commun. math. Phys.9, 192–211 (1968).
Köthe, G.: Topologische lineare Räume. Berlin-Göttingen-Heidelberg: Springer 1960.
Ludwig, G.: Attempt of an axiomatic foundation of quantum mechanics and more general theories II. Commun. math. Phys.4, 331–348 (1967).
—— Attempt of an axiomatic foundation of quantum mechanics and more general theories III. Commun. math. Phys.9, 1–12 (1968).
—— Deutung des Begriffs „physikalische Theorie“ und axiomatische Grundlegung der Hilbertraumstruktur der Quantenmechanik durch Hauptsätze des Messens. Berlin-Heidelberg-New York: Springer 1970.
Maeda, S.: On the symmetry of the modular relation in atomic lattices. J. Sci. Hiroshima Univ., Ser. A 1,29, 165–170 (1965).
Pontrjagin, L.S.: Topologische Gruppen I. Leipzig: B. G. Teubner 1957.
MacLaren, M.D.: Atomic orthocomplemented lattices. Pacific J. Math.14 (1), 597–612 (1964).
— Notes on axioms for quantum mechanics. Report ANL-7065 of the Argonne National Laboratory. Argonne, Illinois (1965).
Schreiner, E.A.: Modular pairs in orthomodular lattices. Pacific J. Math.19 (3), 519–528 (1966).
Stolz, P.: Attempt of an axiomatic foundation of quantum mechanics and more general theories V. Commun. math. Phys.11, 303–313 (1969).
Varadarajan, V. S.: Geometry of quantum theory I. Princeton, New Jersey: 1968.
Zierler, N.: Axiomes for non-relativistic quantum mechanics. Pacific J. Math.11 (2), 1151–1169 (1961).
—— On the lattice of closed subspaces of Hilbertspace. Pacific J. Math.19 (3), 583–586 (1968).
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This paper was supported by the Deutsche Forschungsgemeinschaft.
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Stolz, P. Attempt of an axiomatic foundation of quantum mechanics and more general theories VI. Commun.Math. Phys. 23, 117–126 (1971). https://doi.org/10.1007/BF01877753
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DOI: https://doi.org/10.1007/BF01877753