https://doi.org/10.1140/epjc/s10052-016-4179-5
Regular Article - Theoretical Physics
Beyond gauge theory: positivity and causal localization in the presence of vector mesons
1
CBPF, Rua Dr. Xavier Sigaud 150, Rio de Janeiro, 22290-180, Brazil
2
Institut für Theoretische Physik, FU-Berlin, Arnimallee 14, Berlin, 14195, Germany
* e-mail: schroer@zedat.fu-berlin.de
Received:
5
January
2016
Accepted:
8
June
2016
Published online:
6
July
2016
The Hilbert space formulation of interacting vector-potentials stands is 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 of 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 space-like string direction of its interpolating fields. In contrast to gauge theory, whose direct physical range is limited to a gauge-invariant perturbative S-matrix and local observables, its Hilbert space string-local counterpart is a full-fledged quantum field theory (QFT). The new setting reveals that the Lie structure of self-coupled vector mesons results from perturbative implementation of the causal localization principles of QFT.
© The Author(s), 2016