Charge superselection sectors for scalar QED on the lattice (Q1424265)

In this 31-page paper the authors have dealt with the lattice model of scalar quantum electrodynamics in the Hamiltonian framework. There are 5 sections: Introduction, Scalar QED on the lattice, The observable algebra, Representation of the observable algebra and Charge super-selection structure, and Discussion. After discussing the standard second quantization procedure on the lattice, the field algebra is defined. The observables in terms of field operators are constructed and an abstract definition of observable algebra in terms of generators and relations is given. A \(C^*\)-structure is introduced. All faithful, irreducible and nondegenarate representations are found and a proof of their being labeled by the eigenvalues of the total charge operator is provided. This also has yielded the super-selection structure. After discussing some perspectives of the present research, two appendices are included comprising an example and a unified description for both the bosonic and fermionic matter. There are 20 references. Altogether this is a very good paper dealing with one of the outstanding problem areas in theoretical physics.