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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