Research Article
BibTex RIS Cite
Year 2023, Volume: 41 Issue: 2, 271 - 275, 30.04.2023

Abstract

References

  • REFERENCES
  • [1] Majid S. Foundations of Quantum Group Theory. 1st ed. Cambridge: Cambridge University Press; 1995.[CrossRef]
  • [2] Manin, Y, I. Quantum groups and noncommutative geometry, Montreal Univ. 1988, Preprint.
  • [3] Drinfeld VG. Quantum groups. J Sov Math 1988;41:898-915. [CrossRef]
  • [4] Jimbo M. A q-analogue of U(g[N+1]), Hecke alge-bra and the Yang Baxter equation. Lett Math Phys 1986;11:247-252. [CrossRef]
  • [5] Biedenharn LC. The quantum group SUq(2) and a q-analogue of the boson operators. J Phys A Math Gen 1989;22:873-878. [CrossRef]
  • [6] Macfarlane AJ. On q-analogues of the quantum har-monic oscillator and the quantum group SUq(2). J Phys A Math Gen 1989;22:44581. [CrossRef]
  • [7] Parthasarathy R, Viswanathan KS. A q-analogue of the supersymmetric oscillator and its q-superalge-bra. J Phys A Math Gen 1991;24:613. [CrossRef]
  • [8] Altıntas A, Arık M. The inhomogeneous quantum invariance group of commuting fermions. Open Phys 2007;5:70-82. [CrossRef]
  • [9] Abe E. Hopf Algebras. 1st ed. Cambridge: Cambridge University Press; 1980.
  • [10] Schirrmacher, A. The multiparametric deformation of GL(n) and the covariant differential calculus on the qauntum vector space. Z Phys C Particles Fields 1991;50:321-327. [CrossRef]

Inhomogeneous quantum group of Q-fermions

Year 2023, Volume: 41 Issue: 2, 271 - 275, 30.04.2023

Abstract

In this work, we introduce a nonstandard algebra of q-fermions where q is a nonzero complex deformation parameter for the algebra of the commuting fermions. In order to show that q-fermions provides a proper generalization of the algebra of usual commuting fermions, we prove that there is an inhomogeneous quantum structure associated with q-fermions for a complex number q with |q| = 1.

References

  • REFERENCES
  • [1] Majid S. Foundations of Quantum Group Theory. 1st ed. Cambridge: Cambridge University Press; 1995.[CrossRef]
  • [2] Manin, Y, I. Quantum groups and noncommutative geometry, Montreal Univ. 1988, Preprint.
  • [3] Drinfeld VG. Quantum groups. J Sov Math 1988;41:898-915. [CrossRef]
  • [4] Jimbo M. A q-analogue of U(g[N+1]), Hecke alge-bra and the Yang Baxter equation. Lett Math Phys 1986;11:247-252. [CrossRef]
  • [5] Biedenharn LC. The quantum group SUq(2) and a q-analogue of the boson operators. J Phys A Math Gen 1989;22:873-878. [CrossRef]
  • [6] Macfarlane AJ. On q-analogues of the quantum har-monic oscillator and the quantum group SUq(2). J Phys A Math Gen 1989;22:44581. [CrossRef]
  • [7] Parthasarathy R, Viswanathan KS. A q-analogue of the supersymmetric oscillator and its q-superalge-bra. J Phys A Math Gen 1991;24:613. [CrossRef]
  • [8] Altıntas A, Arık M. The inhomogeneous quantum invariance group of commuting fermions. Open Phys 2007;5:70-82. [CrossRef]
  • [9] Abe E. Hopf Algebras. 1st ed. Cambridge: Cambridge University Press; 1980.
  • [10] Schirrmacher, A. The multiparametric deformation of GL(n) and the covariant differential calculus on the qauntum vector space. Z Phys C Particles Fields 1991;50:321-327. [CrossRef]
There are 11 citations in total.

Details

Primary Language English
Subjects Empirical Software Engineering
Journal Section Research Articles
Authors

Erdoğan Mehmet Özkan 0000-0003-2341-6626

Muttalip Özavşar This is me 0000-0003-1471-6774

Publication Date April 30, 2023
Submission Date April 12, 2021
Published in Issue Year 2023 Volume: 41 Issue: 2

Cite

Vancouver Özkan EM, Özavşar M. Inhomogeneous quantum group of Q-fermions. SIGMA. 2023;41(2):271-5.

IMPORTANT NOTE: JOURNAL SUBMISSION LINK https://eds.yildiz.edu.tr/sigma/