Annales Henri Poincaré

, Volume 4, Issue 6, pp 1137–1167 | Cite as

Charge Superselection Sectors for Scalar QED on the Lattice

Original paper


The lattice model of scalar quantum electrodynamics (Maxwell field coupled to a complex scalar field) in the Hamiltonian framework is discussed. It is shown that the algebra of observables $ \mathcal{O}(\Lambda) $ of this model is a C*-algebra, generated by a set of gauge-invariant elements satisfying the Gauss law and some additional relations. Next, the faithful, irreducible and non-degenerate representations of $ \mathcal{O}(\Lambda) $ are found. They are labeled by the value of the total electric charge, leading to a decomposition of the physical Hilbert space into charge superselection sectors. In the appendices we give a unified description of spinorial and scalar quantum electrodynamics and, as a byproduct, we present an interesting example of weakly commuting operators, which do not commute strongly.


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Copyright information

© Birkhäuser-Verlag 2003

Authors and Affiliations

  1. 1.Center for Theoretical PhysicsPolish Academy of SciencesWarsawPoland
  2. 2.Institut für Theoretische PhysikUniversität LeipzigLeipzigGermany

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