Infinite degeneracy of Landau levels from the Euclidean symmetry with central extension revisited

• URL: http://arxiv.org/abs/2011.06091v2
• Date: Sat, 13 Feb 2021 15:52:26 GMT
• Title: Infinite degeneracy of Landau levels from the Euclidean symmetry with central extension revisited
• Authors: Rajan Murgan
• Abstract summary: The Landau system describes the quantum mechanical motion of a charged particle in a plane with a uniform magnetic field to the plane. We revisit the well-known energy eigenvalues of the system, known as the Landau levels, by exploiting the related $bare(2)$ symmetry algebra.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The planar Landau system which describes the quantum mechanical motion of a charged particle in a plane with a uniform magnetic field perpendicular to the plane, is explored within pedagogical settings aimed at the beginning graduate level. The system is known to possess the Euclidean symmetry in two dimensions with central extension $\bar{E}(2)$. In this paper, we revisit the well-known energy eigenvalues of the system, known as the Landau levels, by exploiting the related $\bar{e}(2)$ symmetry algebra. Specifically, we utilize the Casimir operator and the commutation relations of the generators of the $\bar{E}(2)$ group. More importantly, an algebraic formalism on this topic based on Schwinger's oscillator model of angular momentum is also presented. The dimensions of irreducible representations of the $\bar{E}(2)$ group and their implications on the degeneracy of Landau levels is discussed.

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