RESOLUTION OF CONSTRAINTS AND GAUGE EQUIVALENCE IN ALGEBRAIC SCHRODINGER REPRESENTATION OF QUANTUM ELECTRODYNAMICS

The algebraic formalism of QED is expounded in order to demonstrate bo th the resolution of constraints and to verify gauge equivalence betwe en temporal gauge and Coulomb gauge on the quantum level. In the algeb raic approach energy eigenstates of QED in temporal gauge are represen ted in an algebraic GNS basis. The corresponding Hilbert space is mapp ed into a functional space of generating functional states. The image of the QED-Heisenberg dynamics becomes a functional energy equation fo r these states. In the same manner the Gau ss constraint is mapped int o functional space. By suitable transformations the functional image o f the Coulomb forces is recovered in temporal gauge. The equivalence o f this result with the functional version of QED in Coulomb gauge is d emonstrated. The meaning of the various transformations and their rela tions are illustrated for the case of harmonic oscillators. If applied to QCD this method allows an exact derivation of effective color ''Co ulomb'' forces, in addition it implies a clear conception for the inco rporation of various algebraic representations into the formal Heisenb erg dynamics and establishes the algebraic ''Schrodinger'' equation fo r quantum fields in functional space.