Local aspects of superselection rules
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Abstract
We study a theory of short range forces in terms of local observable quantities; among the superselection structure determined by the algebra of all local observables, to each additive independent charge we associate local observables having a meaning analogous to the regularized integrals of charge density fields over a finite volume. Among other assumptions, we require that parastatistics are absent from the theories considered.
Keywords
Gauge Group Gauge Transformation Double Cone Local Observable Superselection Rule
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References
- 1.Haag, R.: Lille Conference 1957 Les problèmes mathématiques de la théorie quantique des champs. CNRS, Paris (1959)Google Scholar
- 2.Haag, R., Kastler, D.: An algebraic approach to quantum field theory. J. Math. Phys.5, 848 (1964)ADSMathSciNetCrossRefMATHGoogle Scholar
- 3.Doplicher, S., Haag, R., Roberts, J.E.: Fields, observables and Gauge transformations. I. Commun. Math. Phys.13, 1 (1969); II. Commun. Math. Phys.15, 173 (1969)ADSMathSciNetCrossRefMATHGoogle Scholar
- 4.Doplicher, S., Haag, R., Roberts, J.E.: Local observables and particle statistics. I. Commun. Math. Phys.23, 199 (1971); II. Commun. Math. Phys.35, 49 (1974)ADSMathSciNetCrossRefGoogle Scholar
- 5.Buchholz, D., Fredenhagen, K.: Locality and the structure of particle states. Commun. Math. Phys.84, 1–54 (1982)ADSMathSciNetCrossRefMATHGoogle Scholar
- 6.Doplicher, S., Roberts, J.E.: Fields, statistics, and nonabelian Gauge groups. Commun. Math. Phys.28, 331 (1972)ADSMathSciNetCrossRefGoogle Scholar
- 7.Haag, R.: Bemerkungen zum Nahwirkungsprinzip. Ann. Phys.7, 29 (1963)MathSciNetCrossRefGoogle Scholar
- 8.Bourbaki, N.: Espaces vectoriels topologiques, fascicule de résultats. Paris: Hermann 1955MATHGoogle Scholar
- 9.Haag, R., Schroer, B.: Postulates of quantum field theory. J. Math. Phys.3, 248 (1962)ADSMathSciNetCrossRefMATHGoogle Scholar
- 10.Buchholz, D.: Product states for local algebras. Commun. Math. Phys.36, 287 (1974)ADSMathSciNetCrossRefMATHGoogle Scholar
- 11.Summers, S.J.: Normal product states for fermions and twisted duality. (preprint)Google Scholar
- 12.D'Antoni, C., Longo, R.: Interpolation by type I factors and the flip automorphism. J. Funct. Anal. (to appear)Google Scholar
- 13.Takesaki, M.: Duality for crossed products and the structure of von Neumann algebras of type III. Acta Math.131, 249 (1974)MathSciNetCrossRefMATHGoogle Scholar
- 14.Borchers, H.J.: A remark on a theorem of Misra. Commun. Math. Phys.4, 315 (1967)ADSMathSciNetCrossRefMATHGoogle Scholar
- 15.Dixmier, J.: Les algébres d'operateurs dans l'Espace Hilbertien. Paris: Gauthier-Villars 1969MATHGoogle Scholar
- 16.Connes, A., Takesaki, M.: The flow of weights on factors of type III. Tohoku Math. J.29, 473 (1977)MathSciNetCrossRefMATHGoogle Scholar
- 17.Wightman, A.S.: Ann. Inst. Henry Poincaré1, 403 (1964)MathSciNetGoogle Scholar
- 18.Driessler, W.: Duality and absence of locally generated superselection sectors. Commun. Math. Phys.70, 213 (1979)ADSMathSciNetCrossRefMATHGoogle Scholar
- 19.Roberts, J.E.: Local cohomology and superselection sectors. Commun. Math. Phys.51, 107 (1976)ADSCrossRefMATHGoogle Scholar
- 20.Haag, R., Kadison, R.V., Kastler, D.: Nets ofC*-algebras and classification of states. Commun. Math. Phys.16, 11 (1970)MathSciNetCrossRefMATHGoogle Scholar
- 21.Kadison, R.V.: Private communicationGoogle Scholar
- 22.Longo, R.: Algebraic and modular structure of von Neumann algebras of physics. Proceedings A.M.S. Summer Institute on Operator Algebras, Kingston, 1981Google Scholar
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