Construction of Field Algebras with Quantum Symmetry from Local Observables

Details Construction of Field Algebras with Quantum Symmetry from Local Observables Construction of Field Algebras with Quantum Symmetry from Local Observables

1994-01-11

arxiv.org/abs/hep-th/9401042v1

Commun.Math.Phys. 169 (1995) 193-236

Physics

High Energy Physics

High Energy Physics - Theory

50 pages, HUTMP 93-B333

Scientific paper

10.1007/BF02101601

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 $\A$ 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.

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