String-Localized Covariant Quantum Fields

  • Jens Mund
Part of the Progress in Mathematics book series (PM, volume 251)


We present a construction of string-localized covariant free quantum fields for a large class of irreducible (ray) representations of the Poincaré group. Among these are the representations of mass zero and infinite spin, which are known to be incompatible with point-like localized fields. (Based on joint work with B. Schroer and J. Yngvason [13].)


Lorentz Group Direct Integral Decomposition Single Particle Space Schlieder Property Antilinear Involution 
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.
    J.J. Bisognano and E.H. Wichmann: On the duality condition for a Hermitean scalar field. J. Math. Phys. 16:985 (1975).ADSMathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    J. Bros and U. Moschella: Two-point functions and quantum fields in de Sitter universe. Rev. Math. Phys. 8:324 (1996).MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    R. Brunetti, D. Guido and R. Longo: Modular localization and Wigner particles. Rev. Math. Phys. 14:759–786 (2002).MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    D. Buchholz and K. Fredenhagen: Locality and the structure of particle states. Commun. Math. Phys. 84:1–54 (1982).ADSMathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    L. Fassarella and B. Schroer: Wigner particle theory and local quantum physics. J. Phys. A 35:9123–9164 (2002).ADSMathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    G.J. Iverson and G. Mack: Quantum fields and interactions of massless particles: The continuous spin case. Ann. Phys. 64:211–253 (1971).ADSMathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Kunhardt: On infravacua and the localisation of sectors. J. Math. Phys. 39:6353–6363 (1998).ADSMathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    P. Leyland, J. Roberts and D. Testard: Duality for quantum free fields. Unpublished notes, 1978.Google Scholar
  9. 9.
    M. Lüscher: Bosonization in 2 + 1 dimensions. Nucl. Phys. B 326:557–582 (1989).ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    V.F. Müller: Intermediate statistics in two space dimensions in a lattice-regularized Hamiltonian quantum field theory. Z. Phys. C 47:301–310 (1990).MathSciNetCrossRefGoogle Scholar
  11. 11.
    J. Mund: The Bisognano-Wichmann theorem for massive theories. Ann. H. Poincaré. 2:907–926 (2001).MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    J. Mund: Modular localization of massive particles with “any” spin in d = 2+1. J. Math. Phys. 44:2037–2057 (2003).ADSMathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    J. Mund, B. Schroer and J. Yngvason: String-localized quantum fields from Wigner representations. Phys. Lett. B 596:156–162 (2004).ADSMathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    J. Mund, B. Schroer and J. Yngvason: String-localized quantum fields and modular localization. In preparation.Google Scholar
  15. 15.
    M.A. Rieffel and A. Van Daele: A bounded operator approach to Tomita-Takesaki theory. Pacific J. Math. 69 no. 1:187–221 (1977).MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    O. Steinmann: A Jost-Schroer Theorem for String Fields. Commun. Math. Phys. 87:259–264 (1982).ADSMathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    E.P. Wigner: On unitary representations of the inhomogeneous Lorentz group. Ann. Math. 40:149 (1939).ADSMathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    E.P. Wigner: Relativistische Wellengleichungen. Z. Physik 124:665–684 (1948).ADSMathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    F. Wilczek: Quantum mechanics of fractional-spin particles. Phys. Rev. Lett. 49:957–1149 (1982).ADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    D. Yngvason: Zero-mass infinite spin representations of the Poincaré group and quantum field theory. Commun. Math. Phys. 18:195–203 (1970).ADSMathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Birkhäuser Verlag 2007

Authors and Affiliations

  • Jens Mund
    • 1
  1. 1.Instituto de FísicaUniversidade de São PauloSão Paulo, SPBrazil

Personalised recommendations