Communications in Mathematical Physics

, Volume 85, Issue 1, pp 87–98 | Cite as

Localization in algebraic field theory

  • John E. Roberts


The algebra of observables has two distinct local structures. The first, derived from the localization of measurements, gives rise to an additive net structure. The second, derived from the support properties of infinitestimal operations, gives rise to a sheaf structure. It is also shown how an additive net of field algebras acted on by a compact gauge group of the first kind generates an additive net of observable algebras.


Sheaf Structure Double Cone Superselection Sector Observable Algebra Continuous Unitary Representation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 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 1959zbMATHGoogle Scholar
  2. 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)Google Scholar
  3. 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)Google Scholar
  4. 4.
    Buchholz, D., Fredenhagen, K.: Locality and structure of particle states in relativistic quantum theory. Commun. Math. Phys. (to appear)Google Scholar
  5. 5.
    Haag, R., Schroer, B.: Postulates of quantum field theory. J. Math. Phys.3, 248–256 (1962)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Garber, W.-D.: The connexion of duality and causal properties for generalized free fields. Commun. Math. Phys.42, 195–208 (1975)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Borchers, H.J.: Über die Vollständigkeit Lorentzinvarianter Felder in einer zeitartigen Röhre. Nuovo Cimento19, 787–793 (1961)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Glimm, J., Jaffe, A.: Boson quantum field theory models. In: Mathematics of Contemporary Physics, Streater, R.F. (ed.). London, New York: Academic Press 1972Google Scholar
  9. 9.
    Roberts, J.E.: Cross products of von Neumann algebras by group duals. Symp. Math.20, 335–363 (1976)MathSciNetGoogle Scholar
  10. 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)ADSzbMATHGoogle Scholar
  11. 11.
    Araki, H.: Einführung in die axiomatische Quantenfeldtheorie. Lecture Notes ETH, Zürich 1961/62 (unpublished)Google Scholar
  12. 12.
    Haag, R., Kadison, R.V., Kastler, D.: Nets ofC*-algebras and classification of states. Commun. Math. Phys.16, 81–104 (1970)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Doplicher, S., Haag, R., Roberts, J.E.: Fields, observables and gauge transformations. I. Commun. Math. Phys.13, 1–23 (1969)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Borchers, H.J.: Local rings and the connection of spin with statistics. Commun. Math. Phys.1, 281–307 (1965)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Doplicher, S., Haag, R., Roberts, J.E.: Local observables and particle statistics. I. Commun. Math. Phys.23, 199–230 (1971)ADSMathSciNetCrossRefGoogle Scholar
  16. 16.
    Borchers, H.J.: On the converse of the Reeh-Schlieder theorem. Commun. Math. Phys.10, 269–273 (1968)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Borchers, H.J.: A remark on a theorem of B. Misra. Commun. Math. Phys.4, 315–323 (1967)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  18. 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 1980Google Scholar
  19. 19.
    Araki, H., Haag, R., Kastler, D., Takesaki, M.: Extensions of KMS states and chemical potential. Commun. Math. Phys.53, 97–134 (1977)ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • John E. Roberts
    • 1
  1. 1.Fachbereich PhysikUniversität OsnabrückOsnabrückGermany

Personalised recommendations