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Normal product states and nuclearity: New aspects of algebraic quantum field theory

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1136)

Keywords

  • Local Algebra
  • Split Condition
  • Split Property
  • Selfadjoint Extension
  • Charge Operator

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References

  1. Borchers, H.J.: Local rings and the connection of spin with statistics. Commun. Math. Phys. 1 281 (1965)

    CrossRef  ADS  MathSciNet  MATH  Google Scholar 

  2. Doplicher, S., Haag, R., Roberts, J.E.: Local observables and particles statistics I. Commun, Math. Phys. 23, 198 (1971): II. Commun. Math. Phys. 35, 49 (1974)

    CrossRef  ADS  MathSciNet  Google Scholar 

  3. Buchholz, D., Fredenhagen, K.: Locality and the structure of particle states Comm. Math. Phys. 84, 1 (1982)

    CrossRef  ADS  MathSciNet  MATH  Google Scholar 

  4. Buchholz, D.: Product states for local algebras. Commun. Math. Phys. 36 287 (1974)

    CrossRef  ADS  MathSciNet  MATH  Google Scholar 

  5. D'Antoni, C., Longo, R.: Interpolation by type I factors and the flip automorphism. J. Funct. Anal. 51, 361 (1983)

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. Doplicher, S.: Local aspects of superselection rules. Commun. Math. Phys. 85 73 (1982). Doplicher, S., Longo, R.: Local aspects of superselection rules II Commun. Math. Phys 88 399 (1983).

    CrossRef  ADS  MathSciNet  MATH  Google Scholar 

  7. Doplicher, S., Longo, R.: Standard and split inclusions of von Neumann algebras. Invent. Math. 75, 493 (1984).

    CrossRef  ADS  MathSciNet  MATH  Google Scholar 

  8. D'Antoni, C., Fredenhagen, K.: Charge in spacelike cones Commun. Math. Phys. 94 537 (1984)

    CrossRef  ADS  MathSciNet  MATH  Google Scholar 

  9. Driessler, W.: Type of local algebras. Commun. Math. Phys. 53 295 (1977)

    CrossRef  ADS  MathSciNet  MATH  Google Scholar 

  10. Longo, R.: Algebraic and modular structure of von Neumann algebras of Physics. Proceedings of Symposia in PUre Math. 38 551 (1982) part 2

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. Araki,H.: Positive cones, ... Proceedings of the Int. School E. Fermi Course LX, Kastler D. (ed) Soc. Italiana di Fisica. North Holland 1976

    Google Scholar 

  12. Borchers, H.J.: A remark on a theorem of B. Misra. Commun. Math. Phys. 4 315 (1967)

    CrossRef  ADS  MathSciNet  MATH  Google Scholar 

  13. Fredenhagen, K., Hertel, J.: Local algebras of observables and pointlike localized fields. Commun. Math. Phys. 80 555 (1981)

    CrossRef  ADS  MathSciNet  MATH  Google Scholar 

  14. Buchholz,D., Wichmann,E.: Causal independence and Energy-level density of localized states in Quantum Field Theory (preprint)

    Google Scholar 

  15. Haag, R., Swieca J.A.: When does a Quantum Field Theory describe particle? Commun. Math. Phys. 1, 308 (1965)

    CrossRef  ADS  MathSciNet  MATH  Google Scholar 

  16. Weyl, H.: Das asymptotische Verteilungsgesetz der Eigenwerte linearer partieller Differential gleichungen Math. Ann. 71, 441 (1911)

    MathSciNet  MATH  Google Scholar 

  17. Grothendieck, A.: Produits tensoriels topologiques et espaces nucléaires Memoirs A.M.S. 16 (1955)

    Google Scholar 

  18. D'Antoni, C., Fredenhagen, K., Doplicher, S., LOngo, R.: Convergence of local charges and continuity properties for standard W*-inclusions (preprint)

    Google Scholar 

  19. Roberts, J.E. Some applications of dilation invariance to structural questions in the theory of local observables. Comm. Math. Phys. 37 273 (1974).

    CrossRef  ADS  MathSciNet  MATH  Google Scholar 

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© 1985 Springer-Verlag

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D'Antoni, C. (1985). Normal product states and nuclearity: New aspects of algebraic quantum field theory. In: Accardi, L., von Waldenfels, W. (eds) Quantum Probability and Applications II. Lecture Notes in Mathematics, vol 1136. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0074468

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  • DOI: https://doi.org/10.1007/BFb0074468

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15661-1

  • Online ISBN: 978-3-540-39570-6

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