Rational deformations of conformal mechanics

Abstract

We study deformations of the quantum conformal mechanics of De Alfaro-Fubini-Furlan with rational additional potential term generated by applying the generalized Darboux-Crum-Krein-Adler transformations to the quantum harmonic oscillator and by using the method of dual schemes and mirror diagrams. In this way we obtain infinite families of isospectral and non-isospectral deformations of the conformal mechanics model with special values of the coupling constant $g=m(m+1)$, $m\in \mathbb{N}$, in the inverse square potential term, and for each completely isospectral or gapped deformation given by a mirror diagram, we identify the sets of the spectrum-generating ladder operators which encode and coherently reflect its fine spectral structure. Each pair of these operators generates a nonlinear deformation of the conformal symmetry, and their complete sets pave the way for investigation of the associated superconformal symmetry deformations.

37 pages, 3 figures; title changed, version to appear in PRD

References in corpus (15)

• Infinitely many shape invariant potentials and new orthogonal polynomials
• Physics and Mathematics of Calogero particles
• Exceptional orthogonal polynomials, exactly solvable potentials and supersymmetry
• Self-isospectrality, special supersymmetry, and their effect on the band structure
• Solvable rational extensions of the isotonic oscillator
• Baryon Spectrum from Superconformal Quantum Mechanics and its Light-Front Holographic Embedding
• Aharonov-Bohm effect on AdS_2 and nonlinear supersymmetry of reflectionless Poschl-Teller system
• Finite-gap systems, tri-supersymmetry and self-isospectrality
• Effect of scalings and translations on the supersymmetric quantum mechanical structure of soliton systems
• Isoperiodic classical systems and their quantum counterparts
• Perfectly invisible $\mathcal{P}\mathcal{T}$-symmetric zero-gap systems, conformal field theoretical kinks, and exotic nonlinear supersymmetry
• Ground-state isolation and discrete flows in a rationally extended quantum harmonic oscillator
• Hidden superconformal symmetry: Where does it come from?
• Ladder operators for solvable potentials connected with exceptional orthogonal polynomials
• New families of superintegrable systems from k-step rational extensions, polynomial algebras and degeneracies

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• Nonlinear symmetries of perfectly invisible $PT$-regularized conformal and superconformal mechanics systems
• Shape Invariant Potentials in Supersymmetric Quantum Cosmology
• Ladder operators and coherent states for multi-step supersymmetric rational extensions of the truncated oscillator
• Nonlinear supersymmetry as a hidden symmetry
• Hallmarks of tunneling dynamics with broken reflective symmetry
• Do equidistant energy levels necessitate a harmonic potential?
• Exotic nonlinear supersymmetry and integrable systems
• Cosmology as a CFT${}_1$
• Hidden symmetries and nonlinear (super)algebras