Unexplored regions in QFT and the conceptual foundations of the Standard Model

Bert Schroer
June 15, 2010
Massive quantum matter of prescribed spin permits infinitely many possibilities of covariantization in terms of spinorial (undotted/dotted) pointlike fields, whereas massless finite helicity representations lead to large gap in this spinorial spectrum which quantum field theorists usually try to fill by inventing an indefinite metric vectorpotential (Gupta-Bleuler, BRST) outside the quantum theoretic realm. The full range of covariant possiblities (without indefinite metric) is restored if one allows localization along semiinfinite strings. These stringlike potentials fluctuate in the direction of the string (points in a lower de Sitter space) and absorb part of the short distance singularity: there always exists a potential with the smallest short distance dimension allowed by unitarity: sdd=1. In case the interaction with the potential remains linear (QED), there is a delocalization of the massive matter (charged fields, infraparticles) accompanied by a breakdown of the Wigner particle concept (infraparticles), whereas in case of selfinteraction (Yang-Mills, s=2 gravity) the delocalization effect is expected to be much more radical. The third Wigner representation class of positive energy representations is the very large zero mass "infinite spin".family. It carries energy-momentum but is string-localized in much more radical sense than vectorpotentials. The existence of stringlike vectorpotentials is preempted by the Aharonov-Bohm effect in QFT. They also play a crucial role in the formulation of a perturbation theory which aims directly at the physical charged fields. Their role in the the problem behind gluons, quarks and dark matter is presently on a more speculative level. PACS: 11.10.-z, 11.15-q, 11.10Gh, 12.20.-m, 12.38.-t

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