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Independence of local algebras in quantum field theory. (English) Zbl 0197.26303

References:
[1]Haag, R., Kastler, D.: J. Math. Phys.5, 848 (1964). · Zbl 0139.46003 · doi:10.1063/1.1704187
[2]Schlieder, S.: Commun. Math. Phys.13, 216 (1969). · Zbl 0179.58001 · doi:10.1007/BF01645488
[3]Rickart, Charles E.: General theory of Banach algebras. Princeton: Van Nostrand 1960.
[4]Dixmier, Jaques: Les C*-algèbres et leurs représentations. Paris: Gauthier-Villars 1964.
[5]The original version of the proof of lemma 1 needed the assumption that there exists a representation π of 𝔄 12 with π( 𝔄 1)” and π( 𝔄 2)” fulfilling the proposition of Schlieder. The idea of the proof given in this paper is due to Borchers.
[6]Turumaru, T.: Tôhoku Math. J.8, 281 (1956). · Zbl 0072.32903 · doi:10.2748/tmj/1178244952
[7]—- Tôhoku Math. J.16, 111 (1964). · Zbl 0127.07302 · doi:10.2748/tmj/1178243737
[8]Wulfsohn, A.: Bull. Sci. Math.87, 13 (1963).
[9]Okayasu, T.: Tôhoku Math. J.18, 325 (1966). · Zbl 0152.33101 · doi:10.2748/tmj/1178243423