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Construction of field algebras with quantum symmetry from local observables

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It has been discussed earlier that (weak quasi-) quantum groups allow for a 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 the reconstruction of quantum symmetries and algebras of field operators. For every algebraA 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 a local braid relation.

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    Volker Schomerus

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Communicated by A. Jaffe

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Schomerus, V. Construction of field algebras with quantum symmetry from local observables. Commun.Math. Phys. 169, 193–236 (1995). https://doi.org/10.1007/BF02101601

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