# Space- and Time-Like Superselection Rules in Conformal Quantum Field Theory

October 31, 2000

In conformally invariant quantum field theories one encounters besides the
standard DHR superselection theory based on spacelike (Einstein-causal)
commutation relations and their Haag duality another timelike (''Huygens'')
based superselection structure. Whereas the DHR theory based on spacelike
causality of observables confirmed the Lagrangian internal symmetry picture on
the level of the physical principles of local quantum physics, the attempts to
understand the timelike based superselection charges (associated with the
center of the conformal covering group) in terms of timelike localized charges
lead to a more dynamical role of charges outside the DR theorem and even
outside the Coleman-Mandula setting. The ensuing plektonic timelike structure
of conformal theories explains the spectrum of the anomalous scale dimensions
in terms of phase factors in admissable braid group representations, similar to
the explanation of the possible anomalous spin spectrum expected from
stringlike d=1+2 fields with braid group statistics.

open access link

@article{Schroer:2000zx,
author = "Schroer, Bert",
title = "{Space - like and time - like superselection rules in
conformal quantum field theory}",
booktitle = "{Mathematical physics in mathematics and physics: Quantum
and operator algebraic aspects. Proceedings, Conference,
Siena, Italy, June 20-24, 2000}",
journal = "Fields Inst. Commun.",
volume = "30",
year = "2001",
pages = "379-391",
eprint = "hep-th/0010290",
archivePrefix = "arXiv",
primaryClass = "hep-th",
SLACcitation = "%%CITATION = HEP-TH/0010290;%%"
}

Keywords:

*none*