Tiwari, S.C.2025-01-282025-01-282023405779https://dl.bhu.ac.in/ir/handle/123456789/21376Abstract: 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(2,4) 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,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,R)can arise naturally. � 2023, Pleiades Publishing, Ltd.en$SO(3,2)$ groupDirac�s remarkable representationdynamical symmetry groupgroup contractionLandau problemArticlehttps://doi.org/10.1134/S0040577923110016