The Hilbert space formulation of interacting s=1 vector-potentials stands
in an interesting contrast with the point-local Krein space setting of gauge
theory. Already in the absence of interactions the Wilson loop in a Hilbert
space setting has a "topological property" which is missing in the gauge
theoretic description (Haag duality, Aharonov-Bohm effect); the conceptual
differences increase in the presence of interactions. The Hilbert space
positivity weakens the causal localization properties if interacting fields
which results in the replacement of the gauge-variant point-local matter fields
in Krein space by string-local physical fields in Hilbert space. The gauge
invariance of the perturbative S-matrix corresponds to its independence of the
spacelike string direction of its interpolating.fields. In contrast to gauge
theory, whose physical range is limited to gauge invariant perturbative
S-matrix and local observables, its Hilbert space string-local counterpart in
is a full-fledged quantum field theory. The new setting reveals that the
Lie-structure of self-coupled vector mesons results from perturbative
implementation of the causal localization principles of QFT.Comment: 38 page
