# Construction of Field Algebras with Quantum Symmetry from Local Observables

January 11, 1994

It has been discussed earlier that ( weak quasi-) quantum groups allow for
conventional interpretation as internal symmetries in local quantum theory.
From general arguments and explicit examples their consistency with (braid-)
statistics and locality was established. This work addresses to the
reconstruction of quantum symmetries and algebras of field operators. For every
algebra $\cal A$ of observables satisfying certain standard assumptions, an
appropriate quantum symmetry is found. Field operators are obtained which act
on a positive definite Hilbert space of states and transform covariantly under
the quantum symmetry. As a substitute for Bose/Fermi (anti-) commutation
relations, these fields are demonstrated to obey local braid relation.

open access link
Commun.Math.Phys. 169 (1995) 193-236

@article{Schomerus:1994ir,
author = "Schomerus, Volker",
title = "{Construction of field algebras with quantum symmetry
from local observables}",
journal = "Commun. Math. Phys.",
volume = "169",
year = "1995",
pages = "193-236",
doi = "10.1007/BF02101601",
eprint = "hep-th/9401042",
archivePrefix = "arXiv",
primaryClass = "hep-th",
reportNumber = "HUTMP-93-B333",
SLACcitation = "%%CITATION = HEP-TH/9401042;%%"
}

Keywords:

*none*