On the time-dependent oscillator and the nonlinear realizations of the Virasoro group

Akulov V., Catto S., Cebecioglu O., Pashnev A.

PHYSICS LETTERS B, vol.575, pp.137-143, 2003 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 575
  • Publication Date: 2003
  • Doi Number: 10.1016/j.physletb.2003.09.044
  • Journal Name: PHYSICS LETTERS B
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.137-143
  • Kocaeli University Affiliated: Yes


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) similar to SU(1, 1) group embedded in the Virasoro group in a more complicated way. (C) 2003 Elsevier B.V. All rights reserved.