Algebra of Observables and Charge Superselection Sectors for QED on the Lattice | Zendy

Jerzy Kijowski | Zendy; Gerd Rudolph | Zendy; Artur Thielmann | Zendy

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Algebra of Observables and Charge Superselection Sectors for QED on the Lattice

Author(s) -

Jerzy Kijowski,

Gerd Rudolph,

Artur Thielmann

Publication year - 1997

Publication title -

communications in mathematical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.662

H-Index - 152

eISSN - 1432-0916

pISSN - 0010-3616

DOI - 10.1007/s002200050178

Subject(s) - superselection , hilbert space , observable , hamiltonian (control theory) , mathematics , lattice (music) , operator algebra , mathematical physics , physics , charge (physics) , quantum mechanics , algebra over a field , theoretical physics , pure mathematics , mathematical optimization , acoustics

: Quantum Electrodynamics on a finite lattice is investigated within the hamiltonian approach. First, the structure of the algebra of lattice observables is analyzed and it is shown that the charge superselection rule holds. Next, for every eigenvalue of the total charge operator a canonical irreducible representation is constructed and it is proved that all irreducible representations corresponding to a fixed value of the total charge are unique up to unitary equivalence. The physical Hilbert space is by definition the direct sum of these superselection sectors. Finally, lattice quantum dynamics in the Heisenberg picture is formulated and the relation of our approach to gauge fixing procedures is discussed.

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