Schwarzian derivative treatment of the quantum second-order   supersymmetry anomaly, and coupling-constant metamorphosis
  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. 
Mikhail S. Plyushchay
hep-th math-ph math.MP nlin.SI quant-ph