Abstract
Ekstein has shown that causal independence neither implies nor is implied by commutativity in an infinite-dimensional, reducible construction. DeFacio and Taylor have presented a finite-dimensional irreducible example of Ekstein's proposition. Avishai and Ekstein have shown that the original question regarding locality for algebraic quantum field theories remainsopen. We concur with that claim and offer additional arguments. A new denumerably infinite-dimensional, irreducible example is presented here which shows that a sort of “orthogonality” among operators is involved. Some observations on localC*-andW*-algebras are given.
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References
I. E. Segal, inLes Problèmes Mathématiques de la Théorie Quantique des Champs (C.N.R.S., Paris, 1959), pp. 73–107.
I. E. Segal,Mathematical Problems of Relativistic Physics (American Mathematical Society, Providence, Rhode Island, 1963).
E. Prugovecki,Quantum Mechanics in Hilbert Space (Academic Press, 1971), Theorem 6.4, p. 342.
R. Haag and D. Kastler,J. Math. Phys. 4, 848 (1964).
H. Araki, inLocal Quantum Theory, R. Jost, ed. (Academic Press, 1969).
Y. Avishai and H. Ekstein,Found. Phys. 2, 257 (1972).
J. Dixmier,Les algèbres d'opérateurs dans l'espace hilbertien, 2nd ed. (Gauthier-Villars, Paris, 1969).
J. Dixmier,Les C*-algèbres et leurs représentations, 2nd ed. (Gauthier-Villars, Paris, 1969).
S. Schlieder,Commun. Math. Phys. 1, 265 (1965).
S. Schlieder,Commun. Math. Phys. 13, 216 (1969).
K. Kraus,Z. Physik 181, 1 (1964).
H. Roos,Commun. Math. Phys. 16, 238 (1970).
L. J. Landau,Commun. Math. Phys. 13, 246 (1969).
H. Ekstein,Phys. Rev. 184, 1315 (1969);Phys. Rev. D 1, 1851(E) (1970).
B. DeFacio and D. C. Taylor,Phys. Rev. D 8, 2729 (1973).
J. R. Klauder, J. McKenna, and E. J. Woods,J. Math. Phys. 7, 822 (1967).
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Work supported in part by the U.S. Energy Research and Development Administration.
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DeFacio, B. Causal independence in algebraic quantum field theory. Found Phys 5, 229–237 (1975). https://doi.org/10.1007/BF00717439
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DOI: https://doi.org/10.1007/BF00717439