Four dimensional quantum oscillator and magnetic-monopole with U(1)   dynamical group
  By using of an appropriate transformation, it was shown that the quantum system of 4 dimensional simple harmonic oscillator can describe the motion of a charged particle in the presence of a magnetic monopole field. It was shown that the Dirac magnetic monopole has the hidden algebra of U(1) symmetry and by reducing of the dimensions of space, the U(1)*U(1) dynamical group for 4D harmonic oscillator quantum system was obtained. Using the group representation and based on explicit solution of the obtained differential equation, the spectrum of system was calculated. 
Zahra Bakhshi, Hossein Panahi and Goli Golchehre
math-ph math.MP quant-ph