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MiS Preprint
34/2002

Charge Superselection Sectors for Scalar QED on the Lattice

Jerzy Kijowski, Gerd Rudolph and C. Sliwa

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

Received:
Apr 12, 2002
Published:
Apr 12, 2002

Related publications

inJournal
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