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MiS Preprint

Charge Superselection Sectors for Scalar QED on the Lattice

Jerzy Kijowski, Gerd Rudolph and C. Sliwa


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 ${\cal O}({\Lambda})$ 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 ${\cal O}({\Lambda})$ 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.


Related publications

2003 Repository Open Access
C. Sliwa, Jerzy Kijowski and Gerd Rudolph

Charge Superselection Sectors for Scalar QED on the Lattice

In: Annales Henri Poincaré, 4 (2003) 6, pp. 1137-1167