Noncommuting Coordinates, Exotic Particles, and Anomalous Anyons in the Hall Effect

C. Duval; P. A. Horváthy

C. Duval ; P. A. Horváthy

Teoretičeskaâ i matematičeskaâ fizika, Tome 144 (2005) no. 1, pp. 26-34 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Résumé

We review our previous “exotic” particle, together with the more recent anomalous anyon model (which has the arbitrary gyromagnetic factor $g$). The nonrelativistic limit of the anyon generalizes the exotic particle with $g=0$ to any $g$. In a planar electromagnetic field, the Hall effect becomes mandatory for all $g\neq2$ when the field takes some critical value.

Keywords: exotic Galilean symmetry, noncommuting coordinates, Hall effect.

@article{TMF_2005_144_1_a2,
     author = {C. Duval and P. A. Horv\'athy},
     title = {Noncommuting {Coordinates,} {Exotic} {Particles,} and {Anomalous} {Anyons} in the {Hall} {Effect}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {26--34},
     year = {2005},
     volume = {144},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2005_144_1_a2/}
}

TY  - JOUR
AU  - C. Duval
AU  - P. A. Horváthy
TI  - Noncommuting Coordinates, Exotic Particles, and Anomalous Anyons in the Hall Effect
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2005
SP  - 26
EP  - 34
VL  - 144
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2005_144_1_a2/
LA  - ru
ID  - TMF_2005_144_1_a2
ER  -

%0 Journal Article
%A C. Duval
%A P. A. Horváthy
%T Noncommuting Coordinates, Exotic Particles, and Anomalous Anyons in the Hall Effect
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2005
%P 26-34
%V 144
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2005_144_1_a2/
%G ru
%F TMF_2005_144_1_a2

C. Duval; P. A. Horváthy. Noncommuting Coordinates, Exotic Particles, and Anomalous Anyons in the Hall Effect. Teoretičeskaâ i matematičeskaâ fizika, Tome 144 (2005) no. 1, pp. 26-34. http://geodesic.mathdoc.fr/item/TMF_2005_144_1_a2/

Bibliographie
Cité par

[1] L. D. Landau, E. M. Lifshits, Kvantovaya mekhanika. Nerelyativistskaya teoriya, Izd. 4-e, Nauka, M., 1989 ; R. Peierls, Z. Phys., 80 (1933), 763 | MR | DOI | Zbl

[2] S. Girvin, T. Jach, Phys. Rev. B, 29 (1984), 5617 ; G. Dunne, Ann. Phys., 215 (1992), 233 | DOI | MR | DOI | MR | Zbl

[3] F. Ezawa, The Quantum Hall Effects. Field Theoretical Approach and Related Topics, World Scientific, Singapore, 2000 | MR

[4] R. B. Laughlin, Phys. Rev. Lett., 50 (1983), 1395 ; G. Morandi, Quantum Hall Effect. Topological Problems in Condensed-Matter Physics, Monographs and Textbooks in Physical Science. Lecture Notes, 10, Bibliopolis, Napoli, 1988 ; M. Stone (ed.), Quantum Hall Effect, World Scientific, Singapore, 1992 | DOI | MR | Zbl | MR

[5] G. Dunne, R. Jackiw, C. A. Trugenberger, Phys. Rev. D, 41 (1990), 661 ; G. Dunne, R. Jackiw, Nucl. Phys. B (Proc. Suppl.), 33C (1993), 114 | DOI | MR | DOI | MR | Zbl

[6] L. Mittag, M. Stephen, W. Yourgrau, “Variational principles in hydrodynamics”, Variational Principles in Dynamics and Quantum Theory, eds. W. Yourgrau, S. Mandelstam, Saunders, Philadelphia, 1968 ; Republication. Section 13, Dover, N. Y., 1979; L. Onsager, Nuovo Cimento Suppl., 6 (1949), 279 ; H. Lamb, Hydrodynamics, Cambridge Univ. Press, Cambridge, 1932 ; G. Kirchhoff, Vorlesungen über mathematischen Physik: Mechanik, 3rd ed., Teubner, Leipzig, 1876; P. Horváthy, “Noncommuting coordinates in vortex dynamics and in the Hall effect, related to “exotic” Galilean symmetry”, Nonlinear Physics: Theory and Experiment II, Proc. Int. Workshop (Gallipoli, Lecce, Italy, 2002), eds. M. J. Ablowitz, M. Boiti, F. Pempinelli, B. Prinari, World Scientific, River Edge, NJ, 2003, 186 ; ; Noncommuting coordinates in the Hall effect and in vortex dynamics, E-print hep-th/0207075 E-print hep-th/0307175 | MR | DOI | MR | MR | DOI | MR | Zbl

[7] C. Duval, P. A. Horváthy, Phys. Lett. B, 479 (2000), 284 ; J. Phys. A, 34 (2001), 10097 ; P. A. Horváthy, Ann. Phys., 299 (2002), 128 | DOI | MR | Zbl | DOI | MR | Zbl | DOI | MR | Zbl

[8] J.-M. Lévy-Leblond, “Galilei group and Galilean invariance”, Group Theory and Applications, V. II, ed. E. Loebl, Acad. Press, N. Y., 1971, 221 ; Y. Brihaye, C. Gonera, S. Giller, P. Kosiński, Galilean invariance in $2+1$ dimensions, ; J. Lukierski, P. C. Stichel, W. J. Zakrzewski, Ann. Phys., 260 (1997), 224 E-print hep-th/9503046 | DOI | MR | DOI | MR | Zbl

[9] R. Jackiw, V. P. Nair, Phys. Lett. B, 480 (2000), 237 ; E-print hep-th/0003130 | DOI | MR | Zbl

[10] B.-S. Skagerstam, A. Stern, Int. J. Mod. Phys. A, 5 (1990), 1575 ; M. S. Plyushchay, Phys. Lett. B, 248 (1990), 107 ; R. Jackiw, V. P. Nair, Phys. Rev. D, 43 (1991), 1933 ; S. Ghosh, Phys. Lett. B, 338 (1994), 235 | DOI | MR | DOI | MR | DOI | MR | DOI | MR

[11] C. Chou, V. P. Nair, A. Polychronakos, Phys. Lett. B, 304 (1993), 105 | DOI | MR

[12] J. L. Cortés, J. Gamboa, L. Velázquez, Int. J. Mod. Phys. A, 9 (1994), 953 ; S. Ghosh, Phys. Rev. D, 51 (1995), 5827 ; J. L. Cortés, M. S. Plyushchay, Int. J. Mod. Phys. A, 11 (1996), 3331 ; R. Jackiw, Phys. Rev. D, 57 (1998), 2635 | DOI | DOI | DOI | MR | Zbl | DOI

[13] D. K. Maude, M. Potemski, J. C. Portal, Phys. Rev. Lett., 77 (1996), 460 ; D. R. Leadley, R. J. Nicholas, D. K. Maude et al., Phys. Rev. Lett., 79 (1997), 4246 | DOI | DOI

[14] C. Duval, P. A. Horváthy, Phys. Lett. B, 594 (2004), 402 ; E-print hep-th/0402191 | DOI | MR

[15] D. R. Grigore, J. Math. Phys., 37 (1996), 240 ; 460 | DOI | MR | Zbl | MR | Zbl

[16] J.-M. Souriau, Structure des Systèmes Dynamiques. Maitrises de Mathématique, Dunod, Paris, 1970 ; Structure of Dynamical Systems: a Symplectic View of Physics, Birkhäuser, Dordrecht, 1997 | MR | Zbl | Zbl

[17] V. P. Nair, A. P. Polychronakos, Phys. Lett. B, 505 (2001), 267 ; J. Gamboa, M. Loewe, F. Méndez, J. C. Rojas, Phys. Rev. D, 64 (2001), 06701 ; R. Banerjee, Mod. Phys. Lett. A, 17 (2002), 631 ; E-print hep-th/0106280 | DOI | MR | Zbl | DOI | MR | DOI | MR | Zbl

[18] J.-M. Souriau, C. R. Acad. Sci. Paris. Série A, 271 (1970), 1086 ; Ch. Duval, H. H. Fliche, J.-M. Souriau, C. R. Acad. Sci. Paris. Série A, 274 (1972), 1082 ; Ch. Duval, Un modèle de particule à spin dans le champ électromagnétique et gravitationnel extérieur, Thèse de 3e Cycle. Doctoral Thesis, Marseille Univ., Marseille, 1972; J.-M. Souriau, Ann. Inst. H. Poincaré A, 20 (1974), 315 ; Ch. Duval, Ann. Inst. H. Poincaré A, 25 (1976), 345 | MR | MR | MR | MR

[19] W. G. Dixon, Nuovo Cimento, 38 (1965), 1616 | DOI | MR

[20] H. P. Künzle, J. Math. Phys., 13 (1972), 739 | DOI | MR | Zbl

[21] B. S. Skagerstam, A. Stern, Physica Scripta, 24 (1981), 493 ; P. Horváthy, L. Martina, P. Stichel, Phys. Lett. B, 615 (2005), 87 ; E-print hep-th/0412090 | DOI | MR | DOI | MR

Parcourir par

Geodesic

Parcourir par