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Charge Superselection Sectors for Scalar QED on the Lattice

J. Kijowski·G. Rudolph·C. Śliwa
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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 ${\cal O}(Λ)$ 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 ${\cal O}(Λ)$ 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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J. Kijowski, G. Rudolph, C. Śliwa. 2002-03-22. Charge Superselection Sectors for Scalar QED on the Lattice. https://doi.org/10.1007/s00023-003-0158-0

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