Letters in Mathematical Physics

, Volume 43, Issue 4, pp 299–308 | Cite as

On the Structure of the Observable Algebra for QED on the Lattice

  • J. Kijowski
  • G. Rudolph
  • C. Śliwa


We prove that the matter field subalgebra of the observable algebra for QED on a finite lattice is isomorphic to the enveloping algebra of the Lie algebra sl(2N, C), factorized by a certain ideal. Using this result, we give a new proof of the decomposition of the physical Hilbert space into charge superselection sectors.

gauge invariants observable algebra charge superelection sectors 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Kijowski, J., Rudolph, G. and Rudolph, M.: Functional integral of QED in terms of gauge invariant quantities, Lett. Math. Phys 33 (1995), 139–146.CrossRefGoogle Scholar
  2. 2.
    Kijowski, J., Rudolph, G. and Rudolph, M.: Effective bosonic degrees of freedom for one-flavour chromodynamics, Ann. Inst. H. Poincaré (in print).Google Scholar
  3. 3.
    Kijowski, J., Rudolph, G. and Thielman, A.: The algebra of observables and charge superselection sectors for QED on the lattice, Comm. Math. Phys. 188 (1997), 535–564.CrossRefGoogle Scholar
  4. 4.
    Strocchi, F. and Wightman, A.: J. Math. Phys. 15 (1974), 2198.CrossRefGoogle Scholar
  5. 5.
    Strocchi, F.: Comm. Math. Phys. 56 (1977), 57.Google Scholar
  6. 6.
    Strocchi, F.: Phys. Rev. D 17 (1978), 2010.CrossRefGoogle Scholar
  7. 7.
    Fröhlich, J.: Comm. Math. Phys. 66 (1979), 223.Google Scholar
  8. 8.
    Fröhlich, J., Morchio, G. and Strocchi, F.: Ann. of Phys. 119 (1979), 241.CrossRefGoogle Scholar
  9. 9.
    Buchholz, D.: Comm. Math. Phys. 85 (1982), 49; Phys. Lett. B 174 (1986), 331.Google Scholar
  10. 10.
    Fredenhagen, K. and Marcu, M.: Comm. Math. Phys. 92 (1983), 81.Google Scholar
  11. 11.
    Jacobson, N.: Lie Algebras, Dover, New York, 1979.Google Scholar
  12. 12.
    Dixmier, P. J.: Les C *-algèbres et leurs representations, Gauthier-Villars, Paris, 1969.Google Scholar
  13. 13.
    Palev, T. D.: Rep. Math. Phys. 31(3) (1992), 241.Google Scholar

Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • J. Kijowski
    • 1
  • G. Rudolph
    • 2
    • 2
  • C. Śliwa
    • 1
  1. 1.Center for Theoretical PhysicsPolish Academy of Sciences, alWarsawPoland
  2. 2.Institut für Theoretische PhysikUniversität LeipzigLeipzigGermany

Personalised recommendations