OBTAINING DYNAMICAL GROUPS AND QUANTUM DEGREES OF FREEDOM BY USING NOETHER’S THEOREM: THE PLANAR LANDAU SYSTEM

Abstract

The noncompact quantum dynamical group SU(2, 1) and the associated su(2, 1) spectrum-generating algebra of the nonrelativistic planar Landau system are constructively obtained from the classical theory, by considering time-dependent Noether symmetry transformations and along the lines of a procedure recently proposed by Castaños, Frank and López-Peña. For this nonconstrained system in the circular gauge, we have found an explicitly time-dependent Hermitian invariant operator, which is crucial for the correct identification of the number of quantum degrees of freedom.