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Localization in algebraic field theory. (English) Zbl 0509.47036


MSC:

47L90 Applications of operator algebras to the sciences
81T05 Axiomatic quantum field theory; operator algebras
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[1] Haag, R.: Discussion des ”axiomes” et des propriétés asymptotiques d’une théorie des champs locale avec particules composées. 75. Colloques Internationaux du CNRS, Lille 1957. Paris: CNRS 1959
[2] Roberts, J.E.: New light on the mathematical structure of algebraic field theory. Proc. of Symposia in Pure Mathematics, Vol. 38. Am. Math. Soc. (to appear) · Zbl 0528.46056
[3] Roberts, J.E.: The search for quantum differential geometry. Proceedings of the 6th. International Conference on Mathematical Physics, Berlin 1981. In: Lecture Notes in Physics. Berlin, Heidelberg, New York: Springer (to appear)
[4] Buchholz, D., Fredenhagen, K.: Locality and structure of particle states in relativistic quantum theory. Commun. Math. Phys. (to appear) · Zbl 0498.46061
[5] Haag, R., Schroer, B.: Postulates of quantum field theory. J. Math. Phys.3, 248–256 (1962) · Zbl 0125.21903
[6] Garber, W.-D.: The connexion of duality and causal properties for generalized free fields. Commun. Math. Phys.42, 195–208 (1975) · Zbl 0304.46045
[7] Borchers, H.J.: Über die Vollständigkeit Lorentzinvarianter Felder in einer zeitartigen Röhre. Nuovo Cimento19, 787–793 (1961) · Zbl 0111.43204
[8] Glimm, J., Jaffe, A.: Boson quantum field theory models. In: Mathematics of Contemporary Physics, Streater, R.F. (ed.). London, New York: Academic Press 1972 · Zbl 0191.27101
[9] Roberts, J.E.: Cross products of von Neumann algebras by group duals. Symp. Math.20, 335–363 (1976) · Zbl 0441.46053
[10] Driessler, W., Fröhlich, J.: The reconstruction of local observable algebras from the Euclidean Green’s functions of relativistic quantum field theory. Ann. Inst. Henri Poincaré A27, 221–236 (1977) · Zbl 0364.46051
[11] Araki, H.: Einführung in die axiomatische Quantenfeldtheorie. Lecture Notes ETH, Zürich 1961/62 (unpublished)
[12] Haag, R., Kadison, R.V., Kastler, D.: Nets ofC*-algebras and classification of states. Commun. Math. Phys.16, 81–104 (1970) · Zbl 0186.28302
[13] Doplicher, S., Haag, R., Roberts, J.E.: Fields, observables and gauge transformations. I. Commun. Math. Phys.13, 1–23 (1969) · Zbl 0175.24704
[14] Borchers, H.J.: Local rings and the connection of spin with statistics. Commun. Math. Phys.1, 281–307 (1965) · Zbl 0138.45202
[15] Doplicher, S., Haag, R., Roberts, J.E.: Local observables and particle statistics. I. Commun. Math. Phys.23, 199–230 (1971)
[16] Borchers, H.J.: On the converse of the Reeh-Schlieder theorem. Commun. Math. Phys.10, 269–273 (1968) · Zbl 0172.56802
[17] Borchers, H.J.: A remark on a theorem of B. Misra. Commun. Math. Phys.4, 315–323 (1967) · Zbl 0155.32401
[18] Roberts, J.E.: Net cohomology and its applications to field theory. In: Quantum Fields-Algebras, Processes, L. Streit, ed., pp. 240–268. Wien, New York: Springer 1980 · Zbl 0484.57024
[19] Araki, H., Haag, R., Kastler, D., Takesaki, M.: Extensions of KMS states and chemical potential. Commun. Math. Phys.53, 97–134 (1977)
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