Advertisement

Wodzicki residue and anomalies of current algebras

  • Jouko Mickelsson
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 436)

Abstract

The commutator anomalies (Schwinger terms) of current algebras in 3 + 1 dimensions are computed in terms of the Wodzicki residue of pseudodifferential operators; the result can be written as a (twisted) Radul 2-cocycle for the Lie algebra of PSDO's. The construction of the (second quantized) current algebra is closely related to a geometric renormalization of the interaction Hamiltonian H I = JμAμ in gauge theory.

Keywords

Pseudodifferential Operator Central Extension Star Product Current Algebra Affine Algebra 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [Ad]
    M. Adler, Invent. Math. 50, 219 (1979).Google Scholar
  2. [Ar]
    H. Araki in: Contemporary Mathematics, vol. 62, American Mathematical Society, Providence (1987).Google Scholar
  3. [C]
    A. Connes, Commun. Math. Phys. 117, 673 (1988).Google Scholar
  4. [CFNW]
    M. Cederwall, G. Ferretti, B. Nilsson, and A. Westerberg, preprint ITP 93-37 Gothenburg; HEP-TH/940127.Google Scholar
  5. [H]
    L. Hörmander: The Analysis of Linear Partial Differential Operators III. Springer-Verlag, Berlin (1985).Google Scholar
  6. [KV]
    M. Kontsevich and S. Vishik, preprint Max-Planck-Institut für Mathematik, Bonn (April 1994); HEPTH 94 04 46.Google Scholar
  7. [KK]
    O.S. Kravchenko and B.A. Khesin, Funct. Anal. Appl. 25, 83 (1991).Google Scholar
  8. [L]
    Lars-Erik Lundberg, Commun. Math. Phys. 50, 103 (1976).Google Scholar
  9. [LM]
    E. Langmann and J. Mickelsson, work under preparation.Google Scholar
  10. [Ma]
    Yu.I. Manin, J. Sov. Mat. 11, 1 (1979).Google Scholar
  11. [M1]
    J. Mickelsson, Lett. Math. Phys. 28, 97 (1993).Google Scholar
  12. [M2]
    J. Mickelsson: Current Algebras and Groups. Plenum Press, London (1989).Google Scholar
  13. [M,F-Sh]
    J. Mickelsson, Commun. Math. Phys. 97, 361 (1985)Google Scholar
  14. [M,F-Sha]
    L. Faddeev and S. Shatasvili, Theoret. Math. Phys. 60, 770 (1984).Google Scholar
  15. [R]
    A.O. Radul, Funct. Anal. Appl. 25, 25 (1991).Google Scholar
  16. [W]
    M. Wodzicki: Noncommutative residue. In Lecture Notes in Mathematics 1289, ed. by Yu.I. Manin, Springer-Verlag.Google Scholar

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Jouko Mickelsson
    • 1
  1. 1.Royal Institute of TechnologyStockholm

Personalised recommendations