On the Time Dependent Oscillator and the Nonlinear Realizations of the Virasoro Group

Details On the Time Dependent Oscillator and the Nonlinear Realizations of the Virasoro Group On the Time Dependent Oscillator and the Nonlinear Realizations of the Virasoro Group

2003-03-14

arxiv.org/abs/hep-th/0303134v2

Phys.Lett. B575 (2003) 137-143

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX, 12 pages, some references added

Scientific paper

Using the nonlinear realizations of the Virasoro group we construct the action of the Conformal Quantum Mechanics (CQM) with additional harmonic potential. We show that $SL(2,R)$ invariance group of this action is nontrivially embedded in the reparametrization group of the time which is isomorphic to the centerless Virasoro group. We generalize the consideration to the Ermakov systems and construct the action for the time dependent oscillator. Its symmetry group is also the $SL(2,R) \sim SU(1,1)$ group embedded in the Virasoro group in a more complicated way.

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