Full-text resources of PSJD and other databases are now available in the new Library of Science.
Visit https://bibliotekanauki.pl

PL EN


Preferences help
enabled [disable] Abstract
Number of results

Journal

2007 | 5 | 1 | 70-82

Article title

The inhomogeneous quantum invariance group of commuting fermions

Content

Title variants

Languages of publication

EN

Abstracts

EN
We consider a model of d fermions where creation and annihilation operators of different fermions commute. We show that this particle algebra is invariant under an inhomogeneous quantum group.

Publisher

Journal

Year

Volume

5

Issue

1

Pages

70-82

Physical description

Dates

published
1 - 3 - 2007
online
5 - 12 - 2006

Contributors

author
  • Physics Department, Boğaziçi University, Bebek, 34342, Istanbul, Turkey
author
  • Physics Department, Boğaziçi University, Bebek, 34342, Istanbul, Turkey

References

  • [1] M. Jimbo: “A q-Analog of U(gl(N+1)), Hecke Algebra and the Yang-Baxter Equation”, Lett. Math. Phys., Vol. 11, (1986), p. 247. http://dx.doi.org/10.1007/BF00400222[Crossref]
  • [2] S.L. Woronowicz: “Compact Matrix Pseudogroups”, Commun. Math. Phys. Vol. 111, (1987), p. 613. http://dx.doi.org/10.1007/BF01219077[Crossref]
  • [3] Yu.I. Manin: “Quantum Groups and Non-commutative Geometry”, Preprint: Montreal University, CRM-1561, (1988).
  • [4] L.D. Faddeev, N.Y. Reshetikhin and L.A. Takhtajan: “Quantization of Lie groups and Lie algebras”, Leningrad Math. J., Vol. 1, (1990), p. 193.
  • [5] J. Links, A. Forester and M. Karowski: “Bethe Ansatz Solution of a Closed Spin 1 XXZ Heisenberg ChainWith Quantum Algebra Symmetry”, Journal of Mathematical Physics,Vol. 40(2), (1999), pp. 726–735. http://dx.doi.org/10.1063/1.532701[Crossref]
  • [6] V. Pasquer and H. Saleur: “Common Structures Between Finite Systems and Conformal Field Theories Through Quantum Groups”, Nuclear Physics B,Vol. 330, (1990), pp. 523–536. http://dx.doi.org/10.1016/0550-3213(90)90122-T[Crossref]
  • [7] V. Rittenberg and D. Wyler: “Sequences of Z 2 ⊕ Z 2 Graded Lie Algebras and Superalgebras”, J. Math. Phys.,Vol. 19(10), (1978), pp. 2193–2200. http://dx.doi.org/10.1063/1.523552[Crossref]
  • [8] V. Rittenberg and D. Wyler: “Generalized Superalgebras”, Nuclear Physics B,Vol. 139, (1978), pp. 189–202. http://dx.doi.org/10.1016/0550-3213(78)90186-4[Crossref]
  • [9] L.C. Biedenharn and M.A. Lohe: Quantum Group Symmetry and q-Tensor Algebras, World Scientific, Singapore, 1995.
  • [10] M. Arik, U. Kayserilioğlu: “Quantum Invariance Group of Fermions and Bosons”, arXiv:hep-th/0304185.
  • [11] C. Kassel: Quantum Groups, Springer Verlag, New York, 1995.
  • [12] A. Schirrmacher: “The Multiparametric Deformation of GL(n) and the Covariant Differential Calculus on the Quantum Vector Space”, Z. Phys. C-Particles and Fields,Vol. 50, (1991), pp. 321–327. http://dx.doi.org/10.1007/BF01474085[Crossref]
  • [13] M. Arik, S. Gün and A. Yildiz: “Invariance Quantum Group of the Fermionic Oscillator”, Eur. Phys. J. C,Vol. 27, (2003), p. 453. http://dx.doi.org/10.1140/epjc/s2002-01097-x[Crossref]
  • [14] H. Georgi: Lie Algebras in Particle Physics, Westview Press, USA, 1999.
  • [15] A. A. Altintas, M. Arik and N.M. Atakishiyev: “On Unitary Transformations of Orthofermion Algebra That Form a Quantum Group”, Mod. Phys. Lett. A,Vol. 21(18), (2006), pp. 1463–1466. http://dx.doi.org/10.1142/S0217732306019670[Crossref]

Document Type

Publication order reference

Identifiers

YADDA identifier

bwmeta1.element.-psjd-doi-10_2478_s11534-006-0041-y
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.