Klein four-group and Darboux duality in conformal mechanics

@article{Inzunza2019KleinFA,
  title={Klein four-group and Darboux duality in conformal mechanics},
  author={Luis Inzunza and Mikhail S. Plyushchay},
  journal={Physical Review D},
  year={2019}
}
The Klein four-group symmetry of the eigenvalue problem equation for the conformal mechanics model of de Alfaro-Fubini-Furlan (AFF) with coupling constant $g=\nu(\nu+1)\geq -1/4$ undergoes a complete or partial (in the case of half-integer values of $\nu$) breaking at the level of eigenstates of the system. We exploit this breaking of discrete symmetry to construct the dual Darboux transformations which generate the same but spectrally shifted pairs of rationally deformed AFF models for any… 

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