Beyond gauge theory: Hilbert space positivity and causal localization in the presence of vector mesons

Resumo

The Hilbert space formulation of interacting s = 1 vector-potentials stands in an interesting con-trast with the point-local Krein space setting.of gauge theory. Already in the absence of interactionsthe Wilson loop in a Hilbert space setting has a ”topological property” which is missing in the gaugetheoretic description (Haag duality, Aharonov-Bohm effect); the conceptual differences increase in thepresence of interactions.The Hilbert space positivity weakens the causal localization properties if interacting fields whichresults in the replacement of the gauge-variant point-local matter fields in Krein space by string-localphysical fields in Hilbert space. The gauge invariance of the perturbative S-matrix corresponds to itsindependence 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, itsHilbert space string-local counterpart in is a full-fledged quantum field theory (QFT).The new setting reveals that the Lie-structure of self-coupled vector mesons results from pertur-bative implementation of the causal localization principles of QFT.