Communications in Mathematical Physics

, Volume 188, Issue 3, pp 535–564 | Cite as

Algebra of Observables and Charge Superselection Sectors for QED on the Lattice

  • J. Kijowski
  • G. Rudolph
  • A. Thielmann

Abstract:

Quantum Electrodynamics on a finite lattice is investigated within the hamiltonian approach. First, the structure of the algebra of lattice observables is analyzed and it is shown that the charge superselection rule holds. Next, for every eigenvalue of the total charge operator a canonical irreducible representation is constructed and it is proved that all irreducible representations corresponding to a fixed value of the total charge are unique up to unitary equivalence. The physical Hilbert space is by definition the direct sum of these superselection sectors. Finally, lattice quantum dynamics in the Heisenberg picture is formulated and the relation of our approach to gauge fixing procedures is discussed.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • J. Kijowski
    • 1
  • G. Rudolph
    • 2
  • A. Thielmann
    • 3
  1. 1.Center for Theoretical Physics, Polish Academy of Sciences, al. Lotników 32/46, 02-668 Warsaw, PolandPL
  2. 2.Institut für Theoretische Physik, Universität Leipzig, Augustusplatz 10/11, 04109 Leipzig, GermanyDE
  3. 3.Center for Theoretical Physics, Polish Academy of Sciences, al. Lotników 32/46, 02-668 Warsaw, PolandPL

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