Common aspects of q-deformed Lie algebras and fractional calculus

Physica A: Statistical Mechanics and its Applications

Volumn 389, Issue 21, 2010, Pages 4613-4622

  Herrmann, Richard ^a  

^a GigaHedron   (Germany)

Author keywords

Perturbation and fractional calculus methods; q deformed Lie algebras

Indexed keywords

CALCULATIONS; GROUND STATE;

EVEN-EVEN NUCLEI; FRACTIONAL CALCULUS; FRACTIONAL HARMONIC; INTEGER REPRESENTATION; LIE ALGEBRA; ROTATION GROUP; SMOOTH TRANSITIONS; SYMMETRIC ROTORS;

ALGEBRA;

EID: 77956177561     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2010.07.004     Document Type: Article

References (47)

1. D. Bonatsos, and C. Daskaloyannis Quantum groups and their applications in nuclear physics Prog. Part. Nucl. Phys. 43 1999 537 618
2. K.B. Oldham, and J. Spanier The Fractional Calculus 2006 Dover Publications Mineola, New York
3. R. Hilfer Threefold introduction to fractional derivatives R. Klages, G. Radons, I. Sokolov, Anomalous Transport, Foundations and Application 2008 Wiley-VCH Weinheim, Germany 17
4. F. Mainardi Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models 2010 World Scientific Singapore
5. R. Herrmann Fraktionale Infinitesimalrechnung - Eine Einfhrung fr Physiker 2008 BoD Norderstedt, Germany
6. D. Baleanu, and J. Trujillo A new method of finding the fractional EulerLagrange and Hamilton equations within Caputo fractional derivatives Commun. Nonlinear Sci. Num. Sim. 15 5 2010 1111
7. K. Miller, and B. Ross An Introduction to Fractional Calculus and Fractional Differential Equations 1993 Wiley New York
8. N.H. Abel, Solution de quelques problemes a l'aide d'integrales definies, Oeuvres Completes, Vol. 1, Grondahl, Christiana, Norwegen, pp.1618.
9. B. Mandelbrot Fractal Geometry of Nature 1991 Birkhauser
10. Factorization, singular operators and related problems S Samko, A Lebre, A F Dos Santos, Proceedings of the Conference in Honour of Professor Georgii Litvinchuk 2003 Springer Berlin 152
11. A. Raspini Dirac equation with fractional derivatives of order 23 Fizika B 9 2000 49
12. P.J. Zavada Relativistic wave equations with fractional derivatives and pseudo-differential operators J. Appl. Math. 2 4 2002 164
13. N. Laskin Fractional Schrdinger equation Phys. Rev. E 66 2002 056108
14. M. Riesz L'integrale de RiemannLiouville et le problme de Cauchy Acta Math. 81 1949 1
15. R. Herrmann, Continuous differential operators and a new interpretation of the charmonium spectrum, arxiv:nucl-th/0508033 and Herrmann R, Properties of a fractional derivative Schroedinger type wave equation and a new interpretation of the charmonium spectrum, arxiv:math-ph/0510099.
16. E. Goldfain Complexity in quantum-field theory and physics beyond the standard model Chaos Solitons Fractals 28 2006 913
17. V.E. Tarasov, and G.M. Zaslavsky Dynamics with low-level fractionality Physica A 368 2006 399 415
18. S.C. Lim Fractional derivative quantum fields at finite temperatures Physica A 363 2006 269
19. R. Herrmann Gauge invariance in fractional field theories Phys. Lett. A324 2008 5515
20. R. Herrmann Higher-dimensional mixed fractional rotation groups as a basis for dynamic symmetries generating the spectrum of the deformed Nilsson oscillator Physica A 389 4 2010 693
21. R. Herrmann Fractional phase transition in medium size metal clusters Physica A 389 16 2010 3307
22. M. Caputo Linear model of dissipation whose Q is almost frequency independent part II Geophys. J. R. Astr. Soc. 13 1967 529
23. H. Weyl Bemerkungen zum begriff des differentialquotienten gebrochener ordnung Vierteljahresschrift Naturforsch. Ges. Zrich 62 1917 296
24. A.K. Grnwald ber begrenzte derivationen und deren anwendung Z. angew. Math. und Physik 12 1867 441
25. W. Feller Comm. Sem. Mathem. Universite de Lund 1952 73 81
26. V.S. Kiryakova Generalized Fractional Calculus and Applications Pitman Res. Notes in Math. Ser. vol. 301 1994 Longman Harlow co-publ.: J. Wiley and Sons, New York
27. I. Podlubny Fractional Differential Equations 1999 Academic Press New York
28. S.C. Lim Repulsive Casimir force from fractional Neumann boundary conditions Phys. Lett. B679 2009 130
29. G.C. Wu, and J.H. He Fractional calculus of variations in fractal spacetime Nonlinear Sci. Lett. A 1 3 2010 281
30. A. Erzan, and J.-P. Eckmann q-analysis of fractal sets Phys. Rev. Lett. 78 1997 3245 3248
31. P.A.M. Dirac The Principles of Quantum Mechanics 1930 The Clarendon Press Oxford
32. A. Messiah Quantum Mechanics 1968 John Wiley & Sons North-Holland Pub. Co, New York
33. R. Herrmann The fractional symmetric rigid rotor J. Phys. G: Nucl. Part. Phys. 34 2007 607
34. E. Goldfain Fractional dynamics and the TeV regime of field theory Commun. Nonlinear Sci. Numer. Simul. 13 2008 666
35. P.P. Raychev, R.P. Roussev, and F.J. Smirnov Yu The quantum algebra S Uq (2 ) and rotational spectra of deformed nuclei Phys. G. Nucl. Part. Phys. 16 1990 L137
36. R.K. Gupta, J. Cseh, A. Ludu, W. Greiner, and W. Scheid Dynamical symmetry breaking in SU (2 ) model and the quantum group SU (2 ) q J. Phys. G 18 1992 L73
37. C.W. Reich Nucl. Data Sheets 99 2003 753
38. Z. Chunmei, W. Gongqing, and T. Zhenlan Nucl. Data Sheets 83 1998 145
39. D. Frenne, and E. Jacobs Nucl. Data Sheets 89 2000 481
40. B. Singh Nucl. Data Sheets 107 2006 1027
41. G. Gneuss, and W. Greiner Collective potential energy surfaces and nuclear structure Nucl. Phys. A 171 1971 449
42. R.F. Casten, N.V. Zamfir, and D.S. Brenner Universal anharmonic vibrator description of nuclei and critical nuclear phase transitions Phys. Rev. Lett. 71 1993 227
43. D.H. Feng, R. Gilmore, and S.R. Deans Phase transitions and the geometric properties of the interacting boson model Phys. Rev. C 23 1981 1254
44. P. Haapakoski, P. Honkaranta, and P.O. Lipas Projection model for ground bands of eveneven nuclei Phys. Lett. B 31 1970 493
45. A.A. Raduta, A.C. Gheorghe, and A.J. Faessler Remarks on the shape transition from spherical to deformed gamma unstable nuclei Phys. G 31 2005 337
46. J.M. Eisenberg, and W. Greiner Nuclear Models 1987 North Holland Amsterdam
47. W. Greiner, and J. Maruhn Nuclear Models 1996 Springer Berlin