Abstract
In a theory where the local observables are determined by local field algebras as the fixed points under a (a priori noncommutative) group of gauge transformations of the first kind, we show that, if the field algebras possess intermediate type I factors, we can construct observables having the meaning of local charge measurements, and local current algebras in the field algebras.
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Doplicher, S.: Local aspects of superselection rules. Commun. Math. Phys.85, 73 (1982)
Doplicher, S., Haag, R., Roberts, J. E.: Local observables and particle statistics, I. Commun. Math. Phys.23, 198 (1971); II. Commun. Math. Phys.35, 49 (1974)
Buchholz, D., Fredenhagen, K.: Locality and the structure of particle states. Commun. Math. Phys.84, 1 (1982)
Buchholz, D.: Product states for local algebras. Commun. Math. Phys.36, 287 (1974)
Fröhlich, J.: Quantum theory of nonlinear invariant wave equations. In: Invariant wave equations. Lecture Notes in Physics, Vol. 73. Velo, G., Wightman, A.S. (eds.). Berlin, Heidelberg, New York: Springer 1978
D'Antoni, C., Longo, R.: Interpolation by type I factors and the flip automorphism. J. Funct. Anal. (to appear)
Doplicher, S., Longo, R.: Standard and split inclusions of von Neumann algebras (preprint)
Cohn, P. M.: Lie groups. Cambridge: Cambridge University Press 1961
Chevalley, C.: Theory of Lie groups. Princeton, NJ: Princeton University Press 1946
Connes, A.: Caractérisation des espaces vectoriels ordonnés sous-jacents aux algèbres de von Neumann. Ann. Inst. Fourier, Grenoble24, 121 (1974)
Araki, H.: Positive cones, .... Proceedings of the Int. School E. Fermi, Course LX, Kastler, D. (ed.). Soc. Italiana di Fisica. Amsterdam: North-Holland 1976; Recent developments in the theory of operator algebras. Symposia Mathematica XX, Istituto Nazionale di Alta Matematica. New York: Academic Press 1976
Haagerup, U.: The standard form of a von Neumann algebra. Math. Scand.37, 271 (1975)
Takesaki, M.: Tomita's theory of modular Hilbert algebras. In: Lecture Notes in Mathematics, Vol. 128. Berlin, Heidelberg, New York: Springer 1970
Haag, R., Kadison, R. V., Kastler, D.: Nets ofC*-algebra and classification of states. Commun. Math. Phys.16, 11 (1970)
Nelson, E.: Analytic vectors. Ann. Math.70, 572 (1959); see also, Simon, J.: On the integrability of representations of finite dimensional real Lie algebras. Commun. Math. Phys.28, 39 (1972)
Bratteli, O., Robinson, D. W.: Unbounded derivations of von Neumann algebras. Ann. IHP25, 139 (1976)
Gell-Mann, M.: The symmetry group of vector and axial vector currents. Physics1, 63 (1964)
Treiman, S. B., Jackiw, R., Gross, D. J.: Lectures on current algebra and its applications. Princeton: Princeton University Press 1972
Buchholz, D.: in preparation (private communication).
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Communicated by R. Haag
Research supported by Ministero della Pubblica Istruzione and C.N.R.-G.n.a.f.a.
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Doplicher, S., Longo, R. Local aspects of superselection rules. II. Commun.Math. Phys. 88, 399–409 (1983). https://doi.org/10.1007/BF01213216
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DOI: https://doi.org/10.1007/BF01213216