Nonlinear supersymmetry: from classical to quantum mechanics

Abstract

Quantization of the nonlinear supersymmetry faces a problem of a quantum anomaly. For some classes of superpotentials, the integrals of motion admit the corrections guaranteeing the preservation of the nonlinear supersymmetry at the quantum level. With an example of the system realizing the nonlinear superconformal symmetry, we discuss the nature of such corrections and speculate on their possible general origin.

11 pages

References in corpus (9)

• Nonlinear supersymmetry in Quantum Mechanics: algebraic properties and differential representation
• The confluent algorithm in second order supersymmetric quantum mechanics
• Second order SUSY transformations with `complex energies'
• Superconformal mechanics and nonlinear supersymmetry
• A New Family of N-fold Supersymmetry: Type B
• Interaction via reduction and nonlinear superconformal symmetry
• Nonlinear superconformal symmetry of a fermion in the field of a Dirac monopole
• Dolan-Grady Relations and Noncommutative Quasi-Exactly Solvable Systems
• sl(M+1) Construction of Quasi-solvable Quantum M-body Systems

Cited by in corpus (7)

• Nonlinear Supersymmetry for Spectral Design in Quantum Mechanics
• Coherent states for Hamiltonians generated by supersymmetry
• Wronskian formula for confluent second-order supersymmetric quantum mechanics
• Supersymmetric partners of the trigonometric Poschl-Teller potentials
• Trends in supersymmetric quantum mechanics
• Three dimensional N=4 supersymmetric mechanics with Wu-Yang monopole
• Supersymmetry Transformations for Delta Potentials