Geodesic
Dirac representation of the~$SO(3,2)$ group and the~Landau problem
Teoretičeskaâ i matematičeskaâ fizika, Tome 217 (2023) no. 2, pp. 237-259

Voir la notice de l'article provenant de la source Math-Net.Ru

By systematically studying the infinite degeneracy and constants of motion in the Landau problem, we obtain a central extension of the Euclidean group in two dimension as a dynamical symmetry group, and $Sp(2,\mathbb{R})$ as the spectrum generating group, irrespective of the choice of the gauge. The method of group contraction plays an important role. Dirac's remarkable representation of the $SO(3,2)$ group and the isomorphism of this group with $Sp(4,\mathbb{R})$ are revisited. New insights are gained into the meaning of a two-oscillator system in the Dirac representation. It is argued that because even the two-dimensional isotropic oscillator with the $SU(2)$ dynamical symmetry group does not arise in the Landau problem, the relevance or applicability of the $SO(3,2)$ group is invalidated. A modified Landau–Zeeman model is discussed in which the $SO(3,2)$ group isomorphic to $Sp(4,\mathbb{R})$ can arise naturally.
Keywords: dynamical symmetry group, Landau problem, Dirac's remarkable representation
Mots-clés : group contraction, $SO(3,2)$ group. 
@article{TMF_2023_217_2_a0,
     author = {S. C. Tiwari},
     title = {Dirac representation of the~$SO(3,2)$ group and {the~Landau} problem},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {237--259},
     publisher = {mathdoc},
     volume = {217},
     number = {2},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2023_217_2_a0/}
}
TY  - JOUR
AU  - S. C. Tiwari
TI  - Dirac representation of the~$SO(3,2)$ group and the~Landau problem
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2023
SP  - 237
EP  - 259
VL  - 217
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2023_217_2_a0/
LA  - ru
ID  - TMF_2023_217_2_a0
ER  - 
%0 Journal Article
%A S. C. Tiwari
%T Dirac representation of the~$SO(3,2)$ group and the~Landau problem
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2023
%P 237-259
%V 217
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2023_217_2_a0/
%G ru
%F TMF_2023_217_2_a0
S. C. Tiwari. Dirac representation of the~$SO(3,2)$ group and the~Landau problem. Teoretičeskaâ i matematičeskaâ fizika, Tome 217 (2023) no. 2, pp. 237-259. http://geodesic.mathdoc.fr/item/TMF_2023_217_2_a0/