Abstract
Generalizing the Ising model from Z(2) to an arbitrary finite group G we find that the double Hopf algebra D(G) plays the role of the Z(2) × Z(2) symmetry group. Non-Abelian ‘parafermion’ fields are constructed that are irreducible tensor operators with respect to D(G) and that generate amplifying homomorphisms of the observable algebra. The quantum symmetry and braid group statistics of the model are analysed in spirit of the Doplicher-Haag-Roberts programme.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
K. Szlachányi, P. Vecsernyés, Quantum symmetry and braid group statistics in G-spin models, KFKI-1992-08/A, preprint 1992.
R. Dijkgraaf, C. Vafa, E. Verlinde and H. Verlinde, Commun. Math. Phys. 123, 485 (1989).
D. Altschuler and A. Coste, Invariants of 3-manifolds from finite groups, CERN-TH.6204/91, preprint 1991.
R. Dijkgraaf, V. Pasquier and P. Roche, Talk presented at Intern. Coll. on Modern Quantum Field Theory, Tata Institute, 8–14 January 1990.
S. Doplicher, R. Haag and J.E. Roberts, Commun. Math. Phys. 13, 1 (1969).
S. Doplicher, R. Haag and J.E. Roberts, Commun. Math. Phys. 15, 173 (1969).
S. Doplicher, R. Haag and J.E. Roberts, Commun. Math. Phys. 23, 199 (1971); ibid 35, 49 (1974).
S. Doplicher and J.E. Roberts, Bull. Am. Math. Soc. 11, 333 (1984).
S. Doplicher and J.E. Roberts, Ann. Math. 130, 75 (1989).
S. Doplicher and J.E. Roberts, Invent. Math. 98, 157 (1989).
S. Majid, Int. J. Mod. Phys. A5, 1 (1990).
G. Mack and V. Schomerus, Nucl. Phys. B370, 185 (1992).
J. Cuntz, Commun. Math. Phys. 57, 173 (1977).
K. Fredenhagen, K.-H. Rehren and B. Schroer, Commun. Math. Phys. 125, 201 (1989).
R. Longo, Commun. Math. Phys. 126, 217 (1989); ibid 130, 285 (1990).
P. Bántay, Lett. Math. Phys. 22, 187 (1991).
K.-H. Rehren, Braid Group Statistics and their Superselection Rules, in: Algebraic Theory of Superselection Sectors, ed. D. Kastler, p. 333; World Scientific 1990.
K. Szlachányi and P. Vecsernyés, Phys. Lett. 273B, 273 (1991).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer Science+Business Media New York
About this chapter
Cite this chapter
Szlachányi, K. (1993). Order-Disorder Quantum Symmetry in G-Spin Models. In: Osborn, H. (eds) Low-Dimensional Topology and Quantum Field Theory. NATO ASI Series, vol 315. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-1612-9_19
Download citation
DOI: https://doi.org/10.1007/978-1-4899-1612-9_19
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4899-1614-3
Online ISBN: 978-1-4899-1612-9
eBook Packages: Springer Book Archive