Charge Superselection Sectors for Scalar QED on the Lattice
Jerzy Kijowski, Gerd Rudolph, and C. Sliwa
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Submission date: 12. Apr. 2002
published in: Annales Henri Poincaré, 4 (2003) 6, p. 1137-1167
DOI number (of the published article): 10.1007/s00023-003-0158-0
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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 of this model is a -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 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.