Annales Henri Poincaré

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

Charge Superselection Sectors for Scalar QED on the Lattice

Original paper

Abstract.

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.

Keywords

Hilbert Space Scalar Field Electric Charge Lattice Model Quantum Electrodynamic 
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.

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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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