Skip to main content
SpringerLink
Log in
Book cover

Rigorous Quantum Field Theory pp 49–64Cite as

Birkhäuser

Asymptotic Abelianness and Braided Tensor C*-Categories

  • Chapter

Part of the book series: Progress in Mathematics ((PM,volume 251))

Summary

By introducing the concepts of asymptopia and bi-asymptopia, we show how braided tensor C*-categories arise in a natural way. This generalizes constructions in algebraic quantum field theory by replacing local commutativity by suitable forms of asymptotic Abelianness.

Supported in part by the MURST, CNR-GNAFA, INdAM-GNAMPA and the European Union under contract HPRN-CT2002-00280.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. D. Buchholz: The Physical State Space of Quantum Electrodynamics. Comm. Math. Phys. 85:49–71 (1982).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  2. D. Buchholz and S. Doplicher: Exotic Infrared Representations of Interacting Systems. Ann. Inst. H. Poincaré 40:175–184 (1984).

    MathSciNet  MATH  Google Scholar 

  3. D. Buchholz, S. Doplicher, G. Morchio, J.E. Roberts and F. Strocchi: A Model for Charges of Electromagnetic Type. In: Proceedings of the Conference on Operator Algebras and Quantum Field Theory, Rome 1966 (ed.: S. Doplicher et al.), International Press, 1997.

    Google Scholar 

  4. D. Buchholz, S. Doplicher, G. Morchio, J.E. Roberts and F. Strocchi: The Quantum Delocalization of the Electric Charge. Ann. of Phys. 290:53–66 (2001).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  5. D. Buchholz and K. Fredenhagen: Locality and the Structure of Particle States. Comm. Math. Phys. 84:1–54 (1982).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  6. S. Doplicher, R. Haag and J.E. Roberts: Local Observables and Particle Statistics I. Comm. Math. Phys. 23:199–230 (1971) and II. Comm. Math. Phys. 35:49–85 (1974).

    Article  ADS  MathSciNet  Google Scholar 

  7. S. Doplicher and R. Longo: Standard and Split Inclusions of von Neumann Algebras. Invent. Math. 75:493–536 (1984).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  8. S. Doplicher and J.E. Roberts: A New Duality Theory for Compact Groups. Invent. Math. 98:157–218 (1989).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  9. S. Doplicher and J.E. Roberts: Why There is a Field Algebra With a Compact Gauge Group Describing the Superselection Structure in Particle Physics. Comm. Math. Phys. 131:51–107 (1990).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  10. S. Doplicher and M. Spera: Representations Obeying the Spectrum Condition. Comm. Math. Phys. 84:505–513 (1982).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. J. Fröhlich: The Charged Sectors of Quantum Electrodynamics in a Framework of Local Observables. Comm. Math. Phys. 66:223–265 (1979).

    Article  ADS  MathSciNet  Google Scholar 

  12. J. Fröhlich, G. Morchio and F. Strocchi: Charged Sectors and Scattering States in Quantum Electrodynamics. Ann. Phys. 119:241–284 (1979).

    Article  ADS  MathSciNet  Google Scholar 

  13. R. Haag and D. Kastler: An Algebraic Approach to Quantum Field Theory. J. Math. Phys. 5:848–861 (1964).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  14. R. Longo and J.E. Roberts: A Theory of Dimension. K-Theory 11:103–159 (1997).

    Article  MathSciNet  MATH  Google Scholar 

  15. A. Kishimoto: The Representations and Endomorphisms of a Separable Nuclear C*-algebra. Internat. J. Math. 14:313–326 (2003).

    Article  MathSciNet  MATH  Google Scholar 

  16. A. Kishimoto, N. Ozawa and S. Sakai: Homogeneity of the Pure State Space of a Separable C*-Algebra. Canad. Math. Bull. 4:365–372 (2003).

    Article  MathSciNet  MATH  Google Scholar 

  17. J.E. Roberts: Lectures on Algebraic Quantum Field Theory. In: The Algebraic Theory of Superselection Sectors. Introduction and Recent Results (ed.: D. Kastler), pp. 1–112. World Scientific, Singapore, 1990.

    Google Scholar 

  18. D. Salvitti: Generalized Particle Statistics in Two-Dimensions: Examples from the Theory of Free Massive Dirac Field. e-print: hep-th/0507107, and Doctoral Thesis, Rome, 2004.

    Google Scholar 

  19. M. Takesaki: Algebraic Equivalence of Locally Normal Representations. Pacific J. Math. 34:807–816 (1970).

    Article  MathSciNet  MATH  Google Scholar 

  20. J.C. Wick, A.S. Wightman and E.P. Wigner: The Intrinsic Parity of Elementary Particles. Phys. Rev. 88:101–105 (1952).

    Article  ADS  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Theoretische Physik der Universität Göttingen, D-37077, Göttingen, Germany

    Detlev Buchholz

  2. Dipartimento di Matematica, Università di Roma “La Sapienza”, I-00185, Roma, Italy

    Sergio Doplicher

  3. Dipartimento di Fisica dell’Università and INFN, I-56126, Pisa, Italy

    Giovanni Morchio

  4. Dipartimento di Matematica, Università di Roma “Tor Vergata”, I-00133, Roma, Italy

    John E. Roberts

  5. Scuola Normale Superiore and INFN, I-56126, Pisa, Italy

    Franco Strocchi

Authors
  1. Detlev Buchholz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sergio Doplicher
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Giovanni Morchio
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. John E. Roberts
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Franco Strocchi
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institut de Mathématiques de Jussieu, Université Paris 7, 175 rue du Chevaleret, 75013, Paris, France

    Anne Boutet de Monvel

  2. Institut für Theoretische Physik, Universität Göttingen, Friedrich-Hund-Platz 1, 37077, Göttingen, Germany

    Detlef Buchholz

  3. Service de Physique Théorique, CEA/Saclay, Orme des Merisiers, 91191, Gif-sur-Yvette cedex, France

    Daniel Iagolnitzer

  4. Dipartimento di Fisica e Matematica, Università dell’Insubria, Via Valleggio, 11, 22100, Como, Italy

    Ugo Moschella

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Birkhäuser Verlag

About this chapter

Cite this chapter

Buchholz, D., Doplicher, S., Morchio, G., Roberts, J.E., Strocchi, F. (2007). Asymptotic Abelianness and Braided Tensor C*-Categories. In: de Monvel, A.B., Buchholz, D., Iagolnitzer, D., Moschella, U. (eds) Rigorous Quantum Field Theory. Progress in Mathematics, vol 251. Birkhäuser, Basel. https://doi.org/10.1007/978-3-7643-7434-1_5

Download citation

Publish with us

Policies and ethics

Search

Navigation