Construction of Field Algebras with Quantum Symmetry from Local Observables

Volker Schomerus
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;%%" }