Charge Superselection Sectors for Scalar QED on the Lattice

Jerzy Kijowski, Gerd Rudolph, and C. Sliwa

Contact the author: Please use for correspondence this email.
Submission date: 12. Apr. 2002
Pages: 41
published in: Annales Henri Poincaré, 4 (2003) 6, p. 1137-1167 
DOI number (of the published article): 10.1007/s00023-003-0158-0
Bibtex
Download full preprint: PDF (306 kB), PS ziped (238 kB)

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 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.