Schwarzian derivative treatment of the quantum second-order supersymmetry anomaly, and coupling-constant metamorphosis
arXiv:1602.02179 · doi:10.1016/j.aop.2016.12.003
Abstract
A canonical quantization scheme applied to a classical supersymmetric system with quadratic in momentum supercharges gives rise to a quantum anomaly problem described by a specific term to be quadratic in Planck constant. We reveal a close relationship between the anomaly and the Schwarzian derivative, and specify a quantization prescription which generates the anomaly-free supersymmetric quantum system with second order supercharges. We also discuss the phenomenon of a coupling-constant metarmorphosis that associates quantum systems with first-order supersymmetry to the systems with the second-order supercharges.
19 pages. Version accepted for publication in Annals Phys
References in corpus (12)
- Infinitely many shape invariant potentials and new orthogonal polynomials
- Self-isospectrality, special supersymmetry, and their effect on the band structure
- Aharonov-Bohm effect on AdS_2 and nonlinear supersymmetry of reflectionless Poschl-Teller system
- -symmetric invisible defects and confluent Darboux-Crum transformations
- Hidden nonlinear supersymmetry of finite-gap Lame equation
- Position-dependent mass, finite-gap systems, and supersymmetry
- Effect of scalings and translations on the supersymmetric quantum mechanical structure of soliton systems
- Chiral asymmetry in propagation of soliton defects in crystalline backgrounds
- Isospectral Potentials from Modified Factorization
- Soliton defects in one-gap periodic system and exotic supersymmetry
- Null lifts and projective dynamics
- Second-order Supersymmetric Operators and Excited States
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