The DOI matches its Crossref record; 8 of the 8 references it cites were found in a registry or an index.
The quantum group SUq(2) and a q-analogue of the boson operators
Abstract
A new realisation of the quantum group SU q (2) is constructed by means of a q-analogue to the Jordan-Schwinger mapping, determining thereby both the complete representation structure and q-analogues to the Wigner and Racah operators. To achieve this realisation, a new elementary object is defined, a q-analogue to the harmonic oscillator. The uncertainty relation for position and momentum in a q-harmonic oscillator is quite unusual.
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Citations
Cites
Aq-difference analogue of U(g) and the Yang-Baxter equation
Jimbo, M. (1985) · Letters in Mathematical Physics · doi:10.1007/bf00704588 · Cited by 2,600
Angular Momentum in Quantum Physics: Theory and Application
Biedenharn, L. C., Louck, J. D., & Carruthers, P. A. (1984) · Cambridge University Press eBooks · doi:10.1017/cbo9780511759888 · Cited by 869
Self-citationQuantumR matrix for the generalized Toda system
Jimbo, M. (1986) · Communications in Mathematical Physics · doi:10.1007/bf01221646 · Cited by 828
Quantum linear problem for the sine-Gordon equation and higher representations
Kulish, P. P., & Reshetikhin, N. Y. (1983) · Journal of Soviet Mathematics · doi:10.1007/bf01084171 · Cited by 482
REPRESENTATIONS Of THE ALGEBRA Uq(sl(2)), q-ORTHOGONAL POLYNOMIALS AND INVARIANTS OF LINKS
Kirillov, A. N., & Reshetikhin, N. Y. (1990) · Advanced Series in Mathematical Physics · doi:10.1142/9789812798329_0012 · Cited by 297
Quantum group interpretation of some conformal field theories
Gaumé, L. Á., Gómez, C., & Sierra, G. (1989) · Physics Letters B · doi:10.1016/0370-2693(89)90027-0 · Cited by 281
A pattern calculus for tensor operators in the unitary groups
Biedenharn, L. C., & Louck, J. D. (1968) · Communications in Mathematical Physics · doi:10.1007/bf01645800 · Cited by 136
Self-citationRelations for Clebsch–Gordan and Racah coefficients in suq(2) and Yang–Baxter equations
Nomura, M. (1989) · Journal of Mathematical Physics · doi:10.1063/1.528612 · Cited by 86
Cited by
`Nonclassical' states in quantum optics: a `squeezed' review of the first 75 years
Dodonov, V. V. (2002) · Journal of Optics B: Quantum and Semiclassical Optics · doi:10.1088/1464-4266/4/1/201 · Cited by 830
Quantum groups and noncommutative geometry
Majid, S. (2000) · Journal of Mathematical Physics · doi:10.1063/1.533331 · Cited by 92
Metadata
- Authors
- Biedenharn, L. C.
- Venue
- Journal of Physics A: Mathematical and General
- Publisher
- IOP Publishing
- Published
- 1989-09-21
- Volume
- 22
- Issue
- 18
- Pages
- L873-L878
- ISSN
- 0305-4470 (ISSN-L)
- 1361-6447
- OpenAlex
- W1964107355
- Cited by
- 1,509
- References
- 8
- FWCI
- 105.09
- Type
- journal article
- Language
- en
- Open access
- closed
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- Biedenharn, L. C. (1989). The quantum group SUq(2) and a q-analogue of the boson operators. Journal of Physics A: Mathematical and General. https://doi.org/10.1088/0305-4470/22/18/004
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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