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On the algebraic structure of quantum mechanics. (English) Zbl 0171.46804


MSC:

81T08 Constructive quantum field theory

Keywords:

quantum theory
Full Text: DOI

References:

[1] Jordan, P., J. von Neumann, andE. Wigner: Ann. Math.35, 29 (1934). · Zbl 0008.42103 · doi:10.2307/1968117
[2] von Neumann, J.: Mat. Sb.1, 415 (1936).
[3] Birkhoff, G., andJ. von Neumann: Ann. Math.37, 823 (1936). · Zbl 0015.14603 · doi:10.2307/1968621
[4] Segal, I. E.: Ann. Math.48, 930 (1947). · Zbl 0034.06602 · doi:10.2307/1969387
[5] Lowdenslager, D. B.: Proc. Am. Math. Soc.8, 88 (1957). · doi:10.1090/S0002-9939-1957-0084741-9
[6] Sherman, S.: Ann. Math.64, 593 (1956). · Zbl 0075.21802 · doi:10.2307/1969605
[7] Maokey, G. W.: Mathematical foundations of quantum mechanics. New York: Benjamin 1963.
[8] Zierler, N.: Proc. Am. Math. Soc.14, 345 (1963). · doi:10.1090/S0002-9939-1963-0145863-X
[9] —- Pacific J. Math.11, 1151 (1961).
[10] Varadarajan, V. S.: Comm. Pure Appl. Math.15, 189 (1962). · Zbl 0109.44705 · doi:10.1002/cpa.3160150207
[11] Piron, C.: Helv. Phys. Acta37, 439 (1964).
[12] Jauch, J. M., andC. Piron: Helv. Phys. Acta36, 827 (1963).
[13] Pool, J. C. T.: Simultaneous observability and the logic of quantum mechanics. Univ. of Iowa Ph.D. thesis. Department of Physics Report No. 12. · Zbl 0165.28902
[14] Loomis, L. H.: Mem. Am. Math. Soc. No.18 (1955).
[15] Foulis, D. J.: Portugal. Math.21, 65 (1962).
[16] Ramsay, A.: J. Math. Mech.15, 227 (1966).
[17] Wick, G. C., A. S. Wightman, andE. P. Wigner: Phys. Rev.88, 101 (1952). · Zbl 0046.43906 · doi:10.1103/PhysRev.88.101
[18] von Neumann, J.: Mathematical foundations of quantum mechanics. Princeton: Priceton University Press 1956.
[19] Jauch, J. M.: Helv. Phys. Acta37, 293 (1964).
[20] Haag, R., andD. Kastler: J. Math. Phys.5, 848 (1964). · Zbl 0139.46003 · doi:10.1063/1.1704187
[21] Schaefer, H. H.: Topological vector spaces. New York: Macmillan 1966. · Zbl 0141.30503
[22] Edwards, D. A.: Proc. Lond. Math. Soc.14, 399 (1964). · Zbl 0205.12202 · doi:10.1112/plms/s3-14.3.399
[23] Ruston, A. F.: Proc. Cambridge Phil. Soc.53, 576 (1956). · doi:10.1017/S030500410003262X
[24] Grothendieck, A.: Compt. Rend.130, 605 (1950).
[25] Klee, V.: Duke Math. J.22, 263 (1955). · Zbl 0068.09201 · doi:10.1215/S0012-7094-55-02227-4
[26] Miles, P. E.: Trans. Am. Math. Soc.107, 217 (1963).
[27] Bourbaki, N.: Espaces Vectorielles Topologiques. Ch. IV. Actualités Scientifiques et Industrielles Paris: Hermann 1955. · Zbl 0066.35301
[28] Koecher, M.: Am. J. Math.79, 575 (1957). · Zbl 0078.01205 · doi:10.2307/2372563
[29] Rothaus, O.: Abhandl. Math. Seminar Hamburg. Univ.24, 199 (1960).
[30] Vinberg, E. B.: Soviet Math.1, 787 (1960).
[31] Koecher, M.: Math. Ann.148, 244 (1962). · Zbl 0158.28504 · doi:10.1007/BF01470752
[32] Hertnecke, C.: Math. Ann.146, 433 (1962). · Zbl 0143.05202 · doi:10.1007/BF01470657
[33] Koecher, M.: Bull. Am. Math. Soc.68, 374 (1962). · Zbl 0128.03102 · doi:10.1090/S0002-9904-1962-10814-3
[34] Albert, A. A.: Ann. Math.48, 546 (1947). Theorem 14. · Zbl 0029.01003 · doi:10.2307/1969128
[35] Bourbaki, N.: Algèbre Ch. 2. (3éme Ed n ) § 6, No. 5. Actualités Scientifiques et Industrielles. Paris: Hermann 1962. · Zbl 0142.00102
[36] Schatten, R.: Norm ideals of completely continuous operators. Berlin-Göttingen-Heidelberg: Springer 1960. · Zbl 0090.09402
[37] Loewner, C.: Bull. Am. Math. Soc.70, 1 (1964). · Zbl 0196.23701 · doi:10.1090/S0002-9904-1964-11015-6
[38] Stueckelberg, E. C. C., andM. Guenin: Helv. Phys. Acta33, 727 (1960).
[39] Finkelstein, D., J. M. Jauch, S. Schiminovich, andD. Speiser: J. Math. Phys.3, 207 (1962). · doi:10.1063/1.1703794
[40] —- J. Math. Phys.4, 788 (1963). · Zbl 0124.22604 · doi:10.1063/1.1724320
[41] Wightman, A., andS. Schweber: Phys. Rev.98, 812 (1955). · Zbl 0068.22602 · doi:10.1103/PhysRev.98.812
[42] Glimm, J.: Ann. Math.73, 572 (1961). · Zbl 0152.33002 · doi:10.2307/1970319
[43] Araki, H.: J. Math. Phys.5, 1 (1964). · Zbl 0151.44401 · doi:10.1063/1.1704063
[44] Stormer, E.: Trans. Am. Math. Soc.120, 438 (1965).
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