Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Open Physics

formerly Central European Journal of Physics

Editor-in-Chief: Seidel, Sally

Managing Editor: Lesna-Szreter, Paulina

1 Issue per year


IMPACT FACTOR 2017: 0.755
5-year IMPACT FACTOR: 0.820

CiteScore 2017: 0.83

SCImago Journal Rank (SJR) 2017: 0.241
Source Normalized Impact per Paper (SNIP) 2017: 0.537

Open Access
Online
ISSN
2391-5471
See all formats and pricing
More options …
Volume 5, Issue 1

Issues

Volume 13 (2015)

The inhomogeneous quantum invariance group of commuting fermions

Azmi Altintas / Metin Arik
Published Online: 2006-12-05 | DOI: https://doi.org/10.2478/s11534-006-0041-y

Abstract

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.

Keywords: Commuting fermion; quantum group; color supergroup

PACS: 02.20.Uw

  • [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/BF00400222CrossrefGoogle Scholar

  • [2] S.L. Woronowicz: “Compact Matrix Pseudogroups”, Commun. Math. Phys. Vol. 111, (1987), p. 613. http://dx.doi.org/10.1007/BF01219077CrossrefGoogle Scholar

  • [3] Yu.I. Manin: “Quantum Groups and Non-commutative Geometry”, Preprint: Montreal University, CRM-1561, (1988). Google Scholar

  • [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. Google Scholar

  • [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/10.1063/1.532701CrossrefGoogle Scholar

  • [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-TCrossrefGoogle Scholar

  • [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/10.1063/1.523552CrossrefGoogle Scholar

  • [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)90186-4CrossrefGoogle Scholar

  • [9] L.C. Biedenharn and M.A. Lohe: Quantum Group Symmetry and q-Tensor Algebras, World Scientific, Singapore, 1995. Google Scholar

  • [10] M. Arik, U. Kayserilioğlu: “Quantum Invariance Group of Fermions and Bosons”, arXiv:hep-th/0304185. Google Scholar

  • [11] C. Kassel: Quantum Groups, Springer Verlag, New York, 1995. Google Scholar

  • [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/BF01474085CrossrefGoogle Scholar

  • [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-xCrossrefGoogle Scholar

  • [14] H. Georgi: Lie Algebras in Particle Physics, Westview Press, USA, 1999. Google Scholar

  • [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/S0217732306019670CrossrefGoogle Scholar

About the article

Published Online: 2006-12-05

Published in Print: 2007-03-01


Citation Information: Open Physics, Volume 5, Issue 1, Pages 70–82, ISSN (Online) 2391-5471, DOI: https://doi.org/10.2478/s11534-006-0041-y.

Export Citation

© 2006 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Azmi Ali Altıntaṣ and Metin Arık
Physics Letters A, 2008, Volume 372, Number 38, Page 5955
[2]
Azmi Altıntaş, Metin Arık, and Ali Arıkan
Open Physics, 2010, Volume 8, Number 5
[3]
Huseyin Alim, Azmi Ali Altintas, Metin Arik, and Ali Serdar Arikan
International Journal of Theoretical Physics, 2010, Volume 49, Number 3, Page 633
[4]
Azmi Altıntaş, Metin Arık, and Ali Arıkan
Open Physics, 2010, Volume 8, Number 1

Comments (0)

Please log in or register to comment.
Log in