quantum groups

SearchAdvancedHelp

(0.001 seconds)

1—10 of 14 matching pages

1: 17.17 Physical Applications

… ►See Berkovich and McCoy (1998) and Bethuel (1998) for recent surveys. ►Quantum groups also apply $q$-series extensively. Quantum groups are really not groups at all but certain Hopf algebras. They were given this name because they play a role in quantum physics analogous to the role of Lie groups and special functions in classical mechanics. …

2: Tom H. Koornwinder

… ►Koornwinder has published numerous papers on special functions, harmonic analysis, Lie groups, quantum groups, computer algebra, and their interrelations, including an interpretation of Askey–Wilson polynomials on quantum SU(2), and a five-parameter extension (the Macdonald–Koornwinder polynomials) of Macdonald’s polynomials for root systems BC. …

3: Bibliography V

… ►

Representation of Lie Groups and Special Functions. Volume 3: Classical and Quantum Groups and Special Functions. Mathematics and its Applications (Soviet Series), Vol. 75, Kluwer Academic Publishers Group, Dordrecht.

ⓘ

Notes:

Translated from the Russian by V. A. Groza and A. A. Groza

External Links:

ISBN 0-7923-1493-X, MathReview (P. D. F. Ion), ZentralBlatt

Referenced by:

§18.38(iii), Ch.35.

Encodings:

BibTeX

…

4: Bibliography K

… ►

Quantum Groups. Graduate Texts in Mathematics, Vol. 155, Springer-Verlag, New York.

ⓘ

External Links:

ISBN 0-387-94370-6, MathReview (Yu. N. Bespalov), ZentralBlatt

Referenced by:

§17.17.

Encodings:

BibTeX

…

5: Bibliography W

… ►

Group Theory and its Application to the Quantum Mechanics of Atomic Spectra. Pure and Applied Physics. Vol. 5, Academic Press, New York.

ⓘ

Notes:

Expanded and improved ed. Translated from the German by J. J. Griffin.

External Links:

ISBN 0-12-750550-4, MathReview (A. S. Wightman), ZentralBlatt

Referenced by:

§34.12.

Encodings:

BibTeX

…

6: 12.17 Physical Applications

… ► … ►Miller (1974) treats separation of variables by group theoretic methods. Dean (1966) describes the role of PCFs in quantum mechanical systems closely related to the one-dimensional harmonic oscillator. …

7: Bibliography D

… ►

The constrained quantum mechanical harmonic oscillator. Proc. Cambridge Philos. Soc. 62, pp. 277–286.

ⓘ

External Links:

Document, MathReview (T. Erber)

Referenced by:

§12.11(i), §12.11(i), §12.17.

Encodings:

BibTeX

… ►

On the computation of Mathieu functions. J. Engrg. Math. 7, pp. 39–61.

ⓘ

Notes:

Variable-precision Algol program, maximum precision 15D

External Links:

Document, MathReview (C. J. Bouwkamp), ZentralBlatt

Referenced by:

§28.36(ii), §28.36(iii).

Encodings:

BibTeX

… ►

Quantum Fields and Strings: A Course for Mathematicians. Vol. 1, 2. American Mathematical Society, Providence, RI.

ⓘ

Notes:

Material from the Special Year on Quantum Field Theory held at the Institute for Advanced Study, Princeton, NJ, 1996–1997

External Links:

ISBN 0-8218-1198-3, MathReview, ZentralBlatt

Referenced by:

§21.9.

Encodings:

BibTeX

… ►

Monodromy of certain Painlevé-VI transcendents and reflection groups. Invent. Math. 141 (1), pp. 55–147.

ⓘ

External Links:

ISSN 0020-9910, Document, MathReview (Andrei A. Kapaev), ZentralBlatt

Referenced by:

§32.9(iii).

Encodings:

BibTeX

…

8: Bibliography G

… ►

The GAP Group, Centre for Interdisciplinary Research in Computational Algebra, University of St. Andrews, United Kingdom.

ⓘ

Notes:

Groups, Algorithms, Programming: A system for computational discrete algebra with emphasis on computational group theory.

External Links:

GAP

Referenced by:

2nd item.

Encodings:

BibTeX

… ►

Linear Differential Equations and Group Theory from Riemann to Poincaré. 2nd edition, Birkhäuser Boston Inc., Boston, MA.

ⓘ

External Links:

ISBN 0-8176-3837-7, MathReview, ZentralBlatt

Referenced by:

§15.17(v).

Encodings:

BibTeX

… ►

General form of the quantum-defect theory. Phys. Rev. A 19 (4), pp. 1485–1509.

ⓘ

External Links:

Document

Referenced by:

item Greene et al. (1979):, Notations F, Notations F, Notations G.

Encodings:

BibTeX

… ►

Quantum Electrodynamics of Strong Fields: With an Introduction into Modern Relativistic Quantum Mechanics. Texts and Monographs in Physics, Springer.

ⓘ

Referenced by:

§33.22(iv).

Encodings:

BibTeX

…

9: Bibliography

… ►

The Riemann Hypothesis and the Hamiltonian of a Quantum Mechanical System. In Number Theory and Dynamical Systems (York, 1987), M. M. Dodson and J. A. G. Vickers (Eds.), London Math. Soc. Lecture Note Ser., Vol. 134, pp. 153–172.

ⓘ

External Links:

MathReview, ZentralBlatt

Referenced by:

§25.17.

Encodings:

BibTeX

… ►

Normal forms of functions near degenerate critical points, the Weyl groups $A_k,D_k,E_k$ and Lagrangian singularities. Funkcional. Anal. i Priložen. 6 (4), pp. 3–25 (Russian).

ⓘ

Notes:

In Russian. English translation: Functional Anal. Appl., 6(1973), pp. 254–272.

External Links:

MathReview (G. R. Belickii), ZentralBlatt

Referenced by:

§36.2(i).

Encodings:

BibTeX

… ►

Special Functions: Group Theoretical Aspects and Applications. D. Reidel Publishing Co., Dordrecht.

ⓘ

Notes:

Reprinted by Kluwer Academic Publishers, Boston, 2001.

External Links:

ISBN 90-277-1822-9; 1-4020-0319-6, MathReview, ZentralBlatt

Referenced by:

Profile Richard A. Askey, Profile Tom H. Koornwinder.

Encodings:

BibTeX

…

10: Bibliography R

… ►

Research Institute for Symbolic Computation, Hagenberg im Mühlkreis, Austria.

ⓘ

Notes:

Software packages for hypergeometric and $q$-hypergeometric summation, sequences and power series, permutation groups, partition analysis, and difference equations.

External Links:

RISC Combinatorics Group

Referenced by:

6th item.

Encodings:

BibTeX

… ►

Calculation of $3n$-$j$ symbols by Labarthe’s method. International Journal of Quantum Chemistry 63 (1), pp. 57–64.

ⓘ

External Links:

Document

Referenced by:

§34.13.

Encodings:

BibTeX

…