Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2002-03-22
Annales Henri Poincare 4 (2003) 1137-1167
Physics
High Energy Physics
High Energy Physics - Theory
Scientific paper
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.
Kijowski Jerzy
Rudolph Gerd
Sliwa Cezary
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