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Charge Superselection Sectors for Scalar QED on the Lattice.
- Source :
- Annales Henri Poincaré; Dec2003, Vol. 4 Issue 6, p1137-1167, 31p
- Publication Year :
- 2003
-
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 $ \mathcal{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 $ \mathcal{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. [ABSTRACT FROM AUTHOR]
- Subjects :
- LATTICE theory
ELECTRIC charge
ALGEBRA
ELECTRODYNAMICS
Subjects
Details
- Language :
- English
- ISSN :
- 14240637
- Volume :
- 4
- Issue :
- 6
- Database :
- Complementary Index
- Journal :
- Annales Henri Poincaré
- Publication Type :
- Academic Journal
- Accession number :
- 12050629