Yıl 2023,
Cilt: 41 Sayı: 2, 271 - 275, 30.04.2023
Erdoğan Mehmet Özkan
,
Muttalip Özavşar
Kaynakça
- 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
Yıl 2023,
Cilt: 41 Sayı: 2, 271 - 275, 30.04.2023
Erdoğan Mehmet Özkan
,
Muttalip Özavşar
Öz
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.
Kaynakça
- 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]