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Local algebras. A look back at the early years and at some achievements and missed opportunities

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References

  1. Araki, Huzihiro. 1963. A lattice of von Neumann algebras associated with the quantum theory of a free Bose field. J. Math. Phys. 4: 1343-1362

    Article  MATH  MathSciNet  ADS  Google Scholar 

  2. Araki, Huzihiro. 1964a. Von Neumann algebras of local observables für free scalar field J. Math. Phys. 5: 1-13

    Article  MATH  MathSciNet  ADS  Google Scholar 

  3. Araki, Huzihiro. 1964b. Type of von Neumann algebras associated to the free field Prog. Theoret. Phys. 32: 956-965

    Article  MATH  MathSciNet  ADS  Google Scholar 

  4. Becchi, C., A. Rouet and R. Stora. 1974. Phys. Lett. 52B: 344

    ADS  Google Scholar 

  5. Becchi, C., A. Rouet and R. Stora. 1975. Comm. Math. Phys. 42: 127-162

    Article  MathSciNet  ADS  Google Scholar 

  6. Borchers, H.J. 1965a. On the vacuum state in quantum field theory II. Commun. Math. Phys. 1: 57-79

    Article  MATH  MathSciNet  ADS  Google Scholar 

  7. Borchers, H.J. 1965b. Local rings and the connection of spin with statistics. Commun. Math. Phys. 1: 281-307

    Article  MATH  MathSciNet  ADS  Google Scholar 

  8. Bratteli, Ola and Derek W. Robinson. 1979. Operator algebras and quantum statistical mechanics I, Springer Heidelberg, New York

  9. Bratteli, Ola and Derek W. Robinson. 1980. Operator algebras and quantum statistical mechanics II, Springer Heidelberg, New York

  10. Brunetti, Romeo, Klaus Fredenhagen and M. Köhler. 1996. The microlocal spectrum condition and Wick polynomials of free fields on curved spacetimes Commun. Math. Phys. 180 (3): 633-652

    Article  MATH  ADS  Google Scholar 

  11. Buchholz, D. 1982a. The physical state space of quantum electrodynamics Commun. Math. Phys. 85: 49-71

    Article  MATH  MathSciNet  ADS  Google Scholar 

  12. Buchholz, Detley and Klaus Fredenhagen. 1982b. Locality and the structure of particle states Commun. Math. Phys. 84: 1-54

    Article  MATH  MathSciNet  ADS  Google Scholar 

  13. Doplicher, Sergio, Rudolf Haag and John E. Roberts. 1971. Local observables and particle statistics I Commun. Math. Phys. 23: 199-230

    Article  MathSciNet  ADS  Google Scholar 

  14. Doplicher, Sergio, Rudolf Haag and John E. Roberts. 1974. Local observables and particle statistics II Commun. Math. Phys. 35: 49-85

    Article  MathSciNet  ADS  Google Scholar 

  15. Doplicher, Sergio and John E. Roberts. 1984. Compact Lie groups associated with C*-Algebras Bull. Am. Math. Soc. 11: 333-338

    Article  MATH  MathSciNet  Google Scholar 

  16. Doplicher, Sergio and John E. Roberts. 1988. Compact group actions on C*-Algebras Operator Theory 19: 283-305

    MATH  MathSciNet  Google Scholar 

  17. Doplicher, Sergio and John E. Roberts. 1989a. Endomorphisms of C*-algebras, cross products and duality for compact groups Ann. Math. 130: 75-119

    Article  MathSciNet  Google Scholar 

  18. Doplicher, Sergio and John E. Roberts. 1989b. Monoidal C*-categories and a new duality theory for compact groups Invent. Math. 98: 157

    Article  MATH  MathSciNet  ADS  Google Scholar 

  19. Doplicher, Sergio and John E. Roberts. 1990. Why there is a field algebra with a compact gauge group describing the superselection structure in particle physics Commun. Math. Phys. 131: 51-107

    Article  MATH  MathSciNet  ADS  Google Scholar 

  20. Fredenhagen, Klaus, K.H. Rehren and Bert Schroer. 1989. Superselection sectors with braid group statistics and exchange algebras I Commun. Math. Phys. 125: 201-226

    Article  MATH  MathSciNet  ADS  Google Scholar 

  21. Jones, V.F.R. 1983. Index for subfactors Invent. Math. 72: 1-25

    Article  MATH  MathSciNet  ADS  Google Scholar 

  22. Haag, Rudolf. 1954. Lecture Notes Copenhagen CERNT/RH1 53/54

  23. Haag, Rudolf and Bert Schroer. 1962. Postulates of quantum field theory J. Math. Phys. 3: 248-256

    Article  MATH  MathSciNet  ADS  Google Scholar 

  24. Haag, Rudolf and D. Kastler. 1964. An algebraic approach to quantum field theory J. Math. Phys. 5: 848-861

    Article  MATH  MathSciNet  ADS  Google Scholar 

  25. Haag, Rudolf, N.M. Hugenholtz and Marinus Winnink. 1967. On the equilibrium states in quantum statistical mechanics Commun. Math. Phys. 5: 215-236

    Article  MATH  MathSciNet  ADS  Google Scholar 

  26. Haag, Rudolf, D. Kastler and E.B. Trych-Pohlmeyer. 1974. Stability and equilibrium states Comm. Phys. 38: 173-193

    Article  MathSciNet  ADS  Google Scholar 

  27. Haag, Rudolf, H. Narnhofer and U. Stein. 1984. On quantum field theories in gravitational background Commun. Math. Phys. 94: 219-238

    Article  MathSciNet  ADS  Google Scholar 

  28. Haag, Rudolf. 2010. Discussion of the ‘axioms’ and the asymptotic properties of a local field theory with composite particles. Eur. Phys. J. H 35 (3): DOI: 10.1140/epjh/e2010-10041-3

  29. Lehmann, Harry, Kurt Symanzik and Wolfhart Zimmermann. 1955. Zur Formulierung quantisierter Feldtheorien Nuovo Cim. 1 (1): 205-225

  30. Pusz, W. and S.L. Woronowicz. 1978. Passive states and KMS states for general quantum systems Commun. Math. Phys. 58: 273-290

    Article  MathSciNet  ADS  Google Scholar 

  31. Radzikowski, M.J. 1992. The Hadamard Condition and Kay‘s conjecture in axiomatic quantum field theory on curved spacetime. Ph.D. thesis, Princeton University

  32. Takesaki, Masamichi. 1979. Theory of Operator Algebras I. Springer-Verlag, Berlin

  33. Takesaki, Masamichi. 2003a. Theory of Operator Algebras II. Springer-Verlag, Berlin

  34. Takesaki, Masamichi. 2003b. Theory of Operator Algebras III. Springer-Verlag, Berlin

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  1. Waldschmidstrasse 4b, 83727, Schliersee/Neuhaus, Germany

    Rudolf Haag

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Haag, R. Local algebras. A look back at the early years and at some achievements and missed opportunities. EPJ H 35, 255–261 (2010). https://doi.org/10.1140/epjh/e2010-10042-7

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